Skip to main content
SpringerLink
Log in

Partial stability and control: The state-of-the-art and development prospects

  • Reviews
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Problems in bordering fields associated with partial stability and stabilization of nonlinear dynamic systems, including partial stability and stabilization by part of coordinates of the phase vector, are reviewed. They are classified, and their relation with other stability and stabilization problems, including recent ones, are considered. Main development trends in theory and research methods are surveyed and certain results and applications are described. The partial control notion in border disciplines is examined. A long list of references is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Akulenko, L.D., Asymptoticheskie metody optimal’nogo upravleniya (Asymptotic Optimal Control Methods), Moscow: Nauka, 1987.

    Google Scholar 

  2. Aleksandrov, A.Yu., Asymptotic Stability of the Solution of Nonlinear Nonautonomous Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1999, no. 2, pp. 5–9.

  3. Aleksandrov, A.Yu., Stability of a Class of Nonlinear Systems, Prikl. Mat. Mekh., 2000, vol. 64, no.4, pp. 545–550.

    Google Scholar 

  4. Alekseeva, S.A., Vorotnikov, V.I., and Feofanova, V.A., Partial Equiasymptotic Stability of Nonlinear Dynamic Systems, Avtom. Telemekh., 2005, no. 2, pp. 3–16.

  5. Aminov, A.B. and Sirazetdinov, T.K., The Lyapunov Functions Method in Problems of Semistability of Motion, Prikl. Mat. Mekh., 1987, vol. 51, no.5, pp. 709–716.

    Google Scholar 

  6. Anapol’skii, L.Yu. and Chaikin, S.V., Stability in Part of Variables of Relative Equilibrium of an Elastic Satellite, Prikl. Mat. Mekh., 1993, vol. 57, no.2, pp. 67–76.

    Google Scholar 

  7. Anashkin, O.V. and Khapaev, M.M., Partial Stability of Nonlinear Systems of Ordinary Differential Equations with a Small Parameter, Diff. Uravn., 1995, vol. 31, no.3, pp. 371–381.

    Google Scholar 

  8. Andreev, A.S., Asymptotic Stability and Instability of Nonautonomous Systems, Prikl. Mat. Mekh., 1979, vol. 43, no.5, pp. 796–805.

    Google Scholar 

  9. Andreev, A.S., Asymptotic Stability and Instability of the Zero Solution of a Nonautonomous System to Part of Variables, Prikl. Mat. Mekh., 1984, vol. 48, no.5, pp. 707–713.

    Google Scholar 

  10. Andreev, A.S., Study of Partial Asymptotic Stability and Instability via Limiting Equations, Prikl. Mat. Mekh., 1987, vol. 51, no.2, pp. 253–259.

    Google Scholar 

  11. Andreev, A.S., Studies of Partial Asymptotic Stability, Prikl. Mat. Mekh., 1991, vol. 55, no.4, pp. 539–547.

    Google Scholar 

  12. Andreev, A.S., Stability of Equilibrium Positions of a Nonautonomous Mechanical System, Prikl. Mat. Mekh., 1996, vol. 60, no.3, pp. 388–396.

    Google Scholar 

  13. Andreev, A.S. and Pavlikov, S.V., Partial Stability of Nonautonomous Functional Differential Equations, Prikl. Mat. Mekh., 1999, vol. 63, no.1, pp. 3–12.

    Google Scholar 

  14. Andrievskii, B.R. and Fradkov, A.L., Izbrannye glavy teorii avtomaticheskogo upravleniya s primerami na yazyke MATLAB (Selected Topics in Automatic Control Theory and Examples in MATLAB), St. Petersburg: Nauka, 1999.

    Google Scholar 

  15. Andrievskii, B.R. and Fradkov, A.L., Control of Chaos: Methods and Applications. I. Methods, Avtom. Telemekh., 2003, no. 5, pp. 3–45.

  16. Bakan, G.M., Volosov, V.V., and Kussul’, N.N., State Estimation for Continuous Dynamic Systems by the Ellipsoid Method, Kibern. Sist. Analiz, 1996, vol. 32, no.6, pp. 72–91.

    Google Scholar 

  17. Burkov, I.V., Stabilization of Natural Mechanical Systems without Velocity Measurements and Application to Control a Solid, Prikl. Mat. Mekh., 1998, vol. 62, no.6, pp. 923–933.

    Google Scholar 

  18. Vavilov, P.A. and Prokop’ev, V.P., Partial Stability of Motion of Linear Difference Systems, in Ustoichivost’ i nelineinye kolebaniya (Stability and Nonlinear Oscillations), Sverdlovsk: Ural. Gos. Univ., 1986, pp. 3–6.

    Google Scholar 

  19. Vorotnikov, V.I., Partial Stability of Motion of Certain Nonlinear Systems, Prikl. Mat. Mekh., 1979, vol. 43, no.3, pp. 441–450.

    Google Scholar 

  20. Vorotnikov, V.I., Partial Stability of Motion, Prikl. Mat. Mekh., 1988, vol. 52, no.3, pp. 372–385.

    Google Scholar 

  21. Vorotnikov, V.I., Ustoichivost’ dinamicheskikh sistem po otnosheniyu k chasti peremennykh (Stability of Dynamic Systems to Part of Variables), Moscow: Nauka, 1991.

    Google Scholar 

  22. Vorotnikov, V.I., Problems and Investigation Methods of Partial Stability and Stabilization of Motion: Trends, Results, and Specifics, Avtom. Telemekh., 1993, no. 3, pp. 3–62.

  23. Vorotnikov, V.I., Partial Stability Theory, Prikl. Mat. Mekh., 1995, vol. 59, no.4, pp. 553–561.

    Google Scholar 

  24. Vorotnikov, V.I., Barbashin-Krasovskii Theorems in Partial Stability Problems, Dokl. Ross. Akad. Nauk, 1997, vol. 354, no.4, pp. 481–484.

    Google Scholar 

  25. Vorotnikov, V.I., Partial Zero-Controllability of Nonlinear Dynamic Systems, Avtom. Telemekh., 1997, no. 6, pp. 50–63.

  26. Vorotnikov, V.I., Partial Stability Problems, Prikl. Mat. Mekh., 1999, vol. 63, no.5, pp. 736–745.

    Google Scholar 

  27. Vorotnikov, V.I., A Nonlinear Game Problem on Reorientation of an Asymmetric Solid Body, Izv. Ross. Akad. Nauk, Mekh. Tverdogo Tela, 1999, no. 1, pp. 3–18.

  28. Vorotnikov, V.I., Two Classes of Partial Stability Problems: Unification of Concepts and Unified Solvability Conditions, Dokl. Ross. Akad. Nauk, 2002, vol. 384, no.1, pp. 47–51.

    Google Scholar 

  29. Vorotnikov, V.I., Stability and Partial Stability of Equilibrium Positions of Nonlinear Dynamic Systems, Dokl. Ross. Akad. Nauk, 2003, vol. 389, no.3, pp. 332–337.

    Google Scholar 

  30. Vorotnikov, V.I., Coordinate Synchronization of Dynamic Systems, Diff. Uravn., 2004, vol. 40, no.1, pp. 5–23.

    Google Scholar 

  31. Vorotnikov, V.I., Partial Global Asymptotic Stability, Dokl. Ross. Akad. Nauk, 2004, vol. 396, no.3, pp. 295–299.

    Google Scholar 

  32. Vorotnikov, V.I. and Prokop’ev, V.P., Partial Stability of Motion of Linear Systems, Prikl. Mat. Mekh., 1978, vol. 42, no.2, pp. 268–271.

    Google Scholar 

  33. Vorotnikov, V.I. and Rumyantsev, V.V., Ustoichivost’ i upravlenie po chasti koordinat fazovogo vektora dinamicheskikh sistem: teoriya metody i prilozhemiya (Stability and Control of Dynamic systems by Part of Phase Vector Coordinates: Theory, Methods, and Applications), Moscow: Nauchnyi Mir, 2001.

    Google Scholar 

  34. Vyiichich, V.A. and Kozlov, V.V., Lyapunov-Stability to Given State Functions, Prikl. Mat. Mekh., 1991, vol. 55, no.4, pp. 555–559.

    Google Scholar 

  35. Galiullin, A.S., Mukhametzyanov, I.A., Mukharlyamov, R.G., and Furasov, V.D., Postroenie sistem programmnogo dvizheniya (Design of Systems of Programmed Motion), Moscow: Nauka, 1971.

    Google Scholar 

  36. Gal’perin, E.A. and Yaroslavtsev, A.A., Partial Stabilization of Steady Motion of Nonlinear Control Systems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1969, no. 5, pp. 140–147.

  37. Demin, V.G., The Rumyantsev Partial Stability Theorem: Its Application in Celestial Mechanics, Kosm. Issl., 1964, vol. 2, no.5, pp. 416–418.

    Google Scholar 

  38. Demin, V.G., Dvizhenie iskusstvennogo sputnika v netsentral’nom pole tyagoteniya (Motion of an Artificial Satellite in a Noncentral Attraction Field), Moscow: Nauka, 1968.

    Google Scholar 

  39. Demin, V.G. and Furasov, V.D., Partial Stabilization of Control Systems, Prikl. Mat. Mekh., 1976, vol. 40, no.2, pp. 355–359.

    Google Scholar 

  40. Druzhinina, O.V. and Shestakov, A.A., The Generalized Lyapunov Direct Method for Problems of Stability and Attraction of Time Systems, Mat. Sb., 2002, vol. 193, no.10, pp. 17–48.

    Google Scholar 

  41. Zaitsev, V.V., Criteria for the Existence and Estimation of Invariant Constraints on Sets of Autonomous Systems of Differential Equations, Diff. Uravn., 1993, vol. 20, no.5, pp. 766–772.

    Google Scholar 

  42. Zubov, V.I., Matematicheskie metody issledovaniya sistem avtomaticheskogo regulirovaniya (Mathematical Research Methods for Automatic Control Systems), Leningrad: Sudpromgiz, 1959.

    Google Scholar 

  43. Zubov, V.I., Dinamika upravlyaemykh protsessov (Dynamics of Controlled Processes), Moscow: Vysshaya Shkola, 1982.

    Google Scholar 

  44. Zuev, A.L., Partial Stabilization of Nonautonomous Systems by Lyapunov Control Functions, Probl. Upravlen. Informatiki, 2000, vol. 32, no.4, pp. 25–34.

    Google Scholar 

  45. Ignat’ev, A.O., Partial Stability of Motion under Constant Perturbations, Mat. Fiz. Nelineinaya Mekh., 1988, no. 10, pp. 20–25.

  46. Ignat’ev, A.O., Conservation of Uniform Partial Asymptotic Stability, Prikl. Mat. Mekh., 1989, vol. 53, no.1, pp. 167–171.

    Google Scholar 

  47. Ignat’ev, A.O., Partial Stability of Almost-Periodic Systems, Diff. Uravn., 1989, vol. 25, no.8, pp. 1446–1448.

    Google Scholar 

  48. Ignat’ev, A.O., Partial Equiasymptotic Stability, Prikl. Mat. Mekh., 1999, vol. 63, no.5, pp. 871–875.

    Google Scholar 

  49. Ignat’ev, A.O., Partial Stability in Functional Differential Delay Systems, Mekh. Tverdogo Tela, 2000, no. 30, pp. 158–164.

  50. Il’yasov, K., Partial Stability of Hereditary Systems, Mat. Fiz., 1982, no. 31, pp. 32–36.

  51. Il’yasov, K., Partial Stability of the Solutions of Linear Difference Equations, Mat. Fiz., 1984, no. 35, pp. 30–32.

  52. Kadiev, R.I., Sufficient Conditions for the Partial Stability of Linear Stochastic Hereditary Systems, Izv. Vuzov. Mat., 2000, vol. 44, no.6, pp. 75–79.

    Google Scholar 

  53. Kadiev, R.I., Partial Stability of the Solutions of Stochastic Functional Differential Equations in First Approximation, Izv. Vuzov. Mat., 2001, vol. 45, no.5, pp. 30–35.

    Google Scholar 

  54. Kalistratova, M.A., Partial Stability of Delay Systems, Avtom. Telemekh., 1986, no. 5, pp. 32–37.

  55. Karapetyan, A.V., Permanent Rotations of a Heavy Solid on an Absolutely Rough Horizontal Plane, Prikl. Mat. Mekh., 1981, vol. 45, no.5, pp. 808–814.

    Google Scholar 

  56. Karapetyan, A.V., Ustoichivost’ statsionarnykh dvizhenii (Stability of Stationary Motion), Moscow: Editorial, 1998.

    Google Scholar 

  57. Karapetyan, A.V. and Rumyantsev, V.V., Stability of Conservative and Dissipative Systems, Itogi Nauki Tekh., Obshch. Mekh., 1983, vol. 6, pp. 3–127.

    Google Scholar 

  58. Karimov, A.U., Partial Stability under Constant Perturbations, in Mat. Fiz. Elektrodinamika, Moscow: Mosk. Gos. Univ., 1973, pp. 3–10.

    Google Scholar 

  59. Karnishin, S.G., Partial Stability of Functional Differential Equations, in Funktsional’no differentsial’nye uravneniya (Functional Differential Equations), Perm: Perm. Pedag. Inst., 1987.

    Google Scholar 

  60. Kovalev, A.M., Partial Controllability of Dynamic Systems, Prikl. Mat. Mekh., 1993, vol. 57, no.6, pp. 41–50.

    Google Scholar 

  61. Kovalev, A.M., Partial Stability and Stabilization of Dynamic systems, Ukr. Math. Zh., 1995, vol. 47, no.2, pp. 186–193.

    Google Scholar 

  62. Kozlov, V.V., Stability of Equilibrium Positions in a Nonstationary Force Field, Prikl. Mat. Mekh., 1991, vol. 51, no.1, pp. 12–19.

    Google Scholar 

  63. Kolmanovskii, V.B. and Nosov, V.R., Ustoichivost’ i periodicheskie rezhimy reguliruemykh sistem s posledeistviem (Stability and Periodic States of Hereditary Control Systems), Moscow: Nauka, 1981.

    Google Scholar 

  64. Kosov, A.A., K zadache ob ustoichivosti dvizheniya otnositel’no chasti peremennykh: voprosy kachestv. teorii diff. uravnenii (Partial Stability of Motion: A Qualitative Theory of Differential Equations), Novosibirsk: Nauka, 1988.

    Google Scholar 

  65. Krasovskii, N.N., Teoriya upravleniya dvizheniem (Motion Control Theory), Moscow: Nauka, 1968.

    Google Scholar 

  66. Krasovskii, N.N., Igrovye zadachi o vstreche dvizhenii (Game Problems of Counter Motions), Moscow: Nauka, 1970.

    Google Scholar 

  67. Krementulo, V.V., Stabilizatsiya statsionarnykh dvizhenii tverdogo tela pri pomoshchi vrashchayushchikhsya mass (Stabilization of Stationary Motion of a Solid by a Rotating Mass), Moscow: Nauka, 1977.

    Google Scholar 

  68. Krivosheev, Yu.A. and Lutsenko, A.V., Partial Stability of Motion of Linear Systems with Constant and Almost Constant Matrices, Prikl. Mat. Mekh., 1980, vol. 44, no.2, pp. 205–210.

    Google Scholar 

  69. Kurakin, L.G., Stability of a Proper Vortex n-gon, Dokl. Ross. Akad. Nauk, 1994, vol. 335, no.6, pp. 729–731.

    Google Scholar 

  70. Lizunova, M.G., Ob ustoichivosti otnositel’no chasti peremennykh v kriticheskom sluchae pary chisto mnimykh kornei: ustoichivost’ i nelineinye kolebaniya (Partial Stability under a Critical Pair of Purely Imaginary Roots: Stability and Nonlinear Oscillations), Sverdlovsk: Ural. Gos. Univ., 1991.

    Google Scholar 

  71. Lilov, L.K., Partial Stabilization of Stationary Motion of Mechanical Systems, Prikl. Mat. Mekh., 1972, vol. 36, no.6, pp. 977–985.

    Google Scholar 

  72. Lutsenko, A.V. and Stadnikova, L.V., Partial Stability in First Approximation, Diff. Uravn., 1973, vol. 9, no.8, pp. 1530–1533.

    Google Scholar 

  73. Lyapunov, A.M., Issledovanie odnogo iz osobennykh sluchaev zadachi ob ustoichivosti dvizheniya (A Special Case of Stability of Motion), Sobr. Soch. (Collected Works), Moscow: Akad. Nauk SSSR, 1956, vol. 2.

    Google Scholar 

  74. Lyao Syao Sin, Partial Asymptotic Stability of Motion of Linear Systems, Prikl. Mat. Mekh., 1989, vol. 53, no.6, pp. 1034–1035.

    Google Scholar 

  75. Malkin, I.G., Stability of Motion in Lyapunov’s Sense, Mat. Sb., 1938, vol. 3(45), no. 1, pp. 47–100.

    Google Scholar 

  76. Malkin, I.G., Teoriya ustoichivosti dvizheniya (Theory of Stability of Motion), Moscow: Nauka, 1966.

    Google Scholar 

  77. Mamedova, T.F., Asymptotic Equivalence of Differential Equations and Partial Stability of Solutions, Proc. Int. Mat. Conf. “Differential Equations and Their Applications,” Saransk: Saransk. Gos. Univ., 1995.

    Google Scholar 

  78. Martynyuk, A.A., Technical Stability of Motion to a Set of Given Coordinates, Prikl. Mat. Mekh., 1972, vol. 8, no.3, pp. 87–91.

    Google Scholar 

  79. Martynyuk, A.A., Prakticheskaya ustoichivost’ dvizheniya (Practical Stability of Motion), Kiev: Naukova Dumka, 1983.

    Google Scholar 

  80. Martynyuk, A.A., Partial Semistability of Motion, Dokl. Ross. Akad. Nauk, 1992, vol. 324, no.1, pp. 39–41.

    Google Scholar 

  81. Martynyuk, A.A., Semistability—A New Trend in Analysis of Nonlinear Systems, Prikl. Mekh., 1994, vol. 30, no.5, pp. 3–17.

    Google Scholar 

  82. Martynyuk, A.A. and Chernetskaya, L.N., Semistability of Linear Autonomous Systems, Dokl. Akad. Nauk Ukrainy, 1993, no. 8, pp. 17–19.

  83. Martynyuk, A.A. and Chernetskaya, L.N., Semistability of Linear Periodic-Coefficient Systems, Dokl. Akad. Nauk Ukrainy, 1993, no. 11, pp. 61–65.

  84. Matrosov, V.M., Theory of Stability of Motion, Prikl. Mat. Mekh., 1962, vol. 26, no.6, pp. 992–1002.

    Google Scholar 

  85. Matrosov, V.M., Development of the Lyapunov Functions Method in Stability Theory, Tr. II Vses. S” ezda po Teor. i Prikl. Mekh. (Proc. II All-Union Congress: Theoretical and Applied Mechanics), Moscow: Nauka, 1965, vol. 1, pp. 112–125.

    Google Scholar 

  86. Matrosov, V.M., Principles of Comparison with Lyapunov’s Vector Functions. Part 4, Diff. Uravn., 1969, vol. 5, no.12, pp. 2129–2143.

    Google Scholar 

  87. Miroshnik, I.V., Partial Stability and Geometric Problems of Nonlinear Dynamics, Avtom. Telemekh., 2002, no. 11, pp. 39–55.

  88. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complicated Dynamic Systems), St. Petersburg: Nauka, 2000.

    Google Scholar 

  89. Mitropol’skii, Yu.A. and Lykova, O.B., Integral’nye mnogoobraziya v nelineinoi mekhanike (Integral Manifolds in Nonlinear Mechanics), Moscow: Nauka, 1973.

    Google Scholar 

  90. Movchan, A.A., Stability of Processes in Two Metrics, Prikl. Mat. Mekh., 1960, vol. 24, no.6, pp. 988–1001.

    Google Scholar 

  91. Moiseev, N.N. and Rumyantsev, V.V., Dinamika tela s polostyami, soderzhashchimi zhidkost’ (Dynamics of Bodies with Liquid-filled Hollows), Moscow: Nauka, 1965.

    Google Scholar 

  92. Mukharlyamov, R.G., Control of Programmed Partial Motion, Diff. Uravn., 1989, vol. 25, no.8, pp. 938–942.

    Google Scholar 

  93. Nabiullin, M.K., Statsionarnye dvizheniya i ustoichivost’ uprugikh sputnikov (Stationary Motion and Stability of Elastic Satellites), Novosibirsk: Nauka, 1990.

    Google Scholar 

  94. Nosov, V.R. and Furasov, V.D., Stability of Discrete-Time Processes to Given Variables and Convergence of Certain Optimization Algorithms, Zh. Vychisl. Mat. Mat.Fiz., 1979, vol. 19, no.2, pp. 316–328.

    Google Scholar 

  95. Oziraner, A.S., Partial Stability of Motion, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1971, no. 1, pp. 92–100.

  96. Oziraner, A.S., Certain Theorems of the Second Lyapunov Method, Prikl. Mat. Mekh., 1972, vol. 36, no.3, pp. 396–404.

    Google Scholar 

  97. Oziraner, A.S., Partial Asymptotic Stability and Instability, Prikl. Mat. Mekh., 1973, vol. 37, no.4, pp. 659–665.

    Google Scholar 

  98. Oziraner, A.S., Stability of Motion in Critical Cases, Prikl. Mat. Mekh., 1975, vol. 39, no.3, pp. 415–421.

    Google Scholar 

  99. Oziraner, A.S., Stability of Time-Varying Motion in First Approximation, Prikl. Mat. Mekh., 1976, vol. 40, no.3, pp. 424–430.

    Google Scholar 

  100. Oziraner, A.S., Partial Stability under Constant Perturbations, Prikl. Mat. Mekh., 1981, vol. 45, no.3, pp. 419–427.

    Google Scholar 

  101. Oziraner, A.S., Investigation of Partial Stability by Quadratic Forms, Prikl. Mat. Mekh., 1986, vol. 50, no.1, pp. 163–167.

    Google Scholar 

  102. Oziraner, A.S. and Rumyantsev, V.V., The Lyapunov Functions Method in Problems of Partial Stability of Motion, Prikl. Mat. Mekh., 1972, vol. 36, no.2, pp. 364–384.

    Google Scholar 

  103. Petrov, B.N., Rutkovskii, V.Yu., and Zemlyakov, S.D., Adaptivnoe koordinatno-parametricheskoe upravlenie nestatsionarnymi ob”ektami (Adaptive Coordinate-Parametric Control of Time-Varying Systems), Moscow: Nauka, 1980.

    Google Scholar 

  104. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Fizmatlit, 1961.

    Google Scholar 

  105. Prokop’ev, V.P., Partial Stability of Motion in a Critical Case of One Zero Root, Prikl. Mat. Mekh., 1975, vol. 39, no.3, pp. 422–426.

    Google Scholar 

  106. Pyatnitskii, E.S., Design of Stabilization Systems for Programmed Motion of Nonlinear Systems, Avtom. Telemekh., 1993, no. 7, pp. 19–37.

  107. Roitenberg, Ya.N., Avtomaticheskoe upravlenie (Automatic Control), Moscow: Nauka, 1992.

    Google Scholar 

  108. Rubanovskii, V.N. and Rumyantsev, V.V., Stability of Motion of Complex Mechanical Systems, Usp. Mekh., 1979, vol. 2, no.2, pp. 53–79.

    Google Scholar 

  109. Rumyantsev, V.V., Partial Stability of Motion, Vestn. Mosk. Gos. Univ., Mat. Mekh. Fiz. Astronom. Khim., 1957, no. 4, pp. 9–16.

  110. Rumyantsev, V.V., Stability of Equilibrium of a Body with a Liquid-filled Hollow, Dokl. Akad. Nauk SSSR, 1959, vol. 124, no.2, pp. 291–294.

    Google Scholar 

  111. Rumyantsev, V.V., Stability of Rotational Motion of a Liquid-filled Solid, Prikl. Mat. Mekh., 1959, vol. 23, no.6, pp. 1057–1065.

    Google Scholar 

  112. Rumyantsev, V.V., Stability of Motion of a Gyrostat, Prikl. Mat. Mekh., 1961, vol. 25, no.1, pp. 9–16.

    Google Scholar 

  113. Rumyantsev, V.V., Stability of Motion of Solids with Liquid-filled Hollows, Tr. II Vses. s”ezda po teor. prikl. mekh. (Proc. 2 All-Union Congress: Theoretical and Applied Mechanics), Moscow: Nauka, 1965, vol. 1, pp. 57–71.

    Google Scholar 

  114. Rumyantsev, V.V., Ob ustoichivosti statsionarnykh dvizhenii sputnikov (Stability of Stationary Motion of Satellites), Moscow: Vychisl. Tsentr Akad. Nauk SSSR, 1967.

    Google Scholar 

  115. Rumyantsev, V.V., Motion and Stability of an Elastic Body with a Liquid-filled Hollow, Prikl. Mat. Mekh., 1969, vol. 33, no.6, pp. 946–957.

    Google Scholar 

  116. Rumyantsev, V.V., Optimal Stabilization of Control Systems, Prikl. Mat. Mekh., 1970, vol. 34, no.3, pp. 440–456.

    Google Scholar 

  117. Rumyantsev, V.V., Partial Asymptotic Stability and Instability of Motion, Prikl. Mat. Mekh., 1971, vol. 35, no.1, pp. 147–152.

    Google Scholar 

  118. Rumyantsev, V.V., Nekotorye zadachi ob ustoichivosti dvizheniya po otnosheniyu k chasti peremennykh. Mekhanika sploshnoi sredy i rodstvennye problemy analiza (Certain Problems in Partial Stability of Motion. Mechanics of Continuous Media and Allied Problems of Analysis), Moscow: Nauka, 1972.

    Google Scholar 

  119. Rumyantsev, V.V., Optimal Partial Stabilization of Motion, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1993, no. 1, pp. 184–189.

  120. Rumyantsev, V.V. and Oziraner, A.S., Ustoichivost’ i stabilizatsiya dvizheniya po otnosheniyu k chasti peremennykh (Partial Stability and Stabilization of Motion), Moscow: Nauka, 1987.

    Google Scholar 

  121. Rutman, M.A., Boundedness of Solutions of Linear Differential and Differential Difference Equations, Tr. Odes. Gidromet. Inst., 1959, no. 20, pp. 3–7.

  122. Savchenko, A.Ya. and Ignat’ev, A.O., Nekotorye zadachi ustoichivosti neavtonomnykh sistem (Certain Problems in the Stability of Nonautonomous Systems), Kiev: Naukova Dumka, 1989.

    Google Scholar 

  123. Silakov, V.P. and Yudaev, G.S., Partial Stability of Difference Systems, Diff. Uravn., 1975, vol. 11, no.5, pp. 909–913.

    Google Scholar 

  124. Sirazetdinov, T.K., Ustoichivost’ sistem s raspredelennymi parametrami (Stability of Distributed-Parameter Systems), Moscow: Nauka, 1987.

    Google Scholar 

  125. Slyn’ko, V.I., Problems of Semistability of Motion, Prikl. Mekh., 2001, vol. 37, no.12, pp. 125–129.

    Google Scholar 

  126. Smirnov, E.Ya. and Ermolina, M.V., Stabilizatsiya programmnykh dvizhenii mekhanicheskikh sistem po chasti peremennykh: voprosy kachestvennoi teorii differentsial’nykh uravnenii (Partial Stabilization of Programmed Motion of Mechanical Systems: Problems of the Qualitative Theory of Differential Equations), Novosibirsk: Nauka, 1988.

    Google Scholar 

  127. Strogaya, G.V., Partial Stability of Decaying Systems under no Perturbations, Diff. Uravn., 1990, vol. 26, no.11, pp. 1949–1955.

    Google Scholar 

  128. Tereki, I., Partial Stability of Solutions of Linear Autonomous Differential Difference Equations, Stud. Sci. Math. Hung., 1983, vol. 18, nos.2–4, pp. 143–152.

    Google Scholar 

  129. Tereki, I. and Hatvani, L., Partial Stability and Convergence of Motion, Prikl. Mat. Mekh., 1981, vol. 45, no.3, pp. 428–435.

    Google Scholar 

  130. Tereki, I. and Hatvani, L., Asymptotic Interruption under Viscous Friction, Prikl. Mat. Mekh., 1982, vol. 46, no.1, pp. 20–26.

    Google Scholar 

  131. Tereki, I. and Hatvani, L., A Lyapunov Function of Mechanical Energy, Prikl. Mat. Mekh., 1985, vol. 49, no.6, pp. 894–899.

    Google Scholar 

  132. Tuan Bu, Partial Stability in First Approximation, Prikl. Mat. Mekh., 1980, vol. 44, no.2, pp. 211–220.

    Google Scholar 

  133. Fradkov, A.L., Adaptivnoe upravlenie v slozhnykh sistemakh (Adaptive Control for Complex Systems), Moscow: Nauka, 1990.

    Google Scholar 

  134. Fradkov, A.L., Investigation of Physical Systems by Feedback, Avtom. Telemekh., 1999, no. 3, pp. 213–230.

  135. Fradkov, A.L., Kiberneticheskaya fizika: printsipy i primery (Cybernetical Physics: Principles and Examples), St. Petersburg: Nauka, 2003.

    Google Scholar 

  136. Furasov, V.D., Ustoichivost’ dvizheniya, otsenki i stabilizatsiya (Stability of Motion, Estimation, and Stabilization), Moscow: Nauka, 1977.

    Google Scholar 

  137. Furasov, V.D., Ustoichivost’ i stabilizatsiya diskretnykh protsessov (Stability and Stabilization of Discrete Processes), Moscow: Nauka, 1982.

    Google Scholar 

  138. Khapaev, M.M., Usrednenie v teorii ustoichivosti, (Averaging in Stability Theory), Moscow: Nauka, 1986.

    Google Scholar 

  139. Hatvani, L., Certain Stability Criteria with Two Lyapunov Functions, Prikl, Mat. Mekh., 1975, vol. 39, no.1, pp. 172–177. (Errata: Prikl. Mat. Mekh., 1976, vol. 40, no. 2, pp. 251.)

    Google Scholar 

  140. Hatvani, L., Application of Differential Inequalities in Stability Theory, Vestn. Mosk. Gos. Univ., Mat. Mekh., 1975, no. 3, pp. 83–89.

  141. Chudinov, K.M., Partial Stability of Linear Autonomous Hereditary Systems, Izv. Vuzov. Mat., 2004, vol. 48, no.6, pp. 72–78.

    Google Scholar 

  142. Sharov, V.F., Partial Stability and Stabilization of Stochastic Systems, Avtom. Telemekh., 1978, no. 11, pp. 63–71.

  143. Shchennikov, V.N., Partial Stability of Differential Systems with Homogeneous Right Sides, Diff. Uravn., 1984, vol. 20, no.9, pp. 1645–1649.

    Google Scholar 

  144. Shchennikov, V.N., Partial Stability in the Critical Case of 2k Purely Imaginary Roots, in Differentsial’nye i integral’nye uravneniya: metody topologicheskoi dinamiki (Differential and Integral Equations: Methods of Topological Dynamics), Gor’kii: Gor’kovsk. Gos. Univ., 1985.

    Google Scholar 

  145. Shchennikov, V.N., Metody sravneniya i metody Lyapunova (Comparison and Lyapunov Methods), Saransk: Mordovsk. Gos. Univ., 1990.

    Google Scholar 

  146. Yudaev, G.S., Partial Stability, Diff. Uravn., 1975, vol. 11, no.6, pp. 1023–1029.

    Google Scholar 

  147. Yudaev, G.S., Stability of Stochastic Differential Equations, Prikl. Mat. Mekh., 1977, vol. 41, vol. 3, pp. 430–435.

    Google Scholar 

  148. Yurkov, A.V., Stabilization of Motion of Mechanical System by Indirect Partial Control, in Voprosy kachestvennoii teorii differents. uravnenii (Problems of Quatitative Theory of Differential Equations), Novosibirsk: Nauka, 1988, pp. 270–272.

    Google Scholar 

  149. Yakubovich, V.A., Optimal Suppression of Interval Oscillations with a Given Output of a System, Dokl. Ross. Akad. Nauk, 1994, vol. 337, no.3, pp. 323–327.

    Google Scholar 

  150. Abed, E.H., Gover, R.E., Goldberg, A.J., and Wolk, S.I., Nonlinear and Stochastic Stability Problems in Gated Radar Range Trackers, Stoch. Theor. Contr. Lect. Notes. Control Int. Sci., 2002, vol. 280, pp. 1–17.

    Google Scholar 

  151. Akinyele, O., On Partial Stability of Differential Equations with Time Delay, Ann. Math. Pure Appl. (IV), 1979, vol. 121, pp. 351–372.

    Google Scholar 

  152. Akinyele, O., Necessary Conditions for the Nonuniform Partial Stability for Delay Systems, Rend. Acc. Naz. del Lincei. Cl. Sci. Fis. Mat. Natur. (8), 1979, vol. 66, nos.3–4, pp. 509–515.

    Google Scholar 

  153. Akinyele, O., On Nonuniform Partial Stability and Perturbations for Delay Systems, Rend. Acc. Naz. del Lincei. Cl. Sci. Fis. Mat. Natur. (8)., 1980, vol. 67, nos.l–2, pp. 39–44.

    Google Scholar 

  154. Akinyele, O., On the Partial Stability of the Nonlinear Abstract Cauchy Problem, Riv. Mat. Univ. Parma. (IV), 1980, vol. 6, pp. 81–88.

    Google Scholar 

  155. Akinyele, O., On Partial Boundedness of Differential Equations with Time Delay, Riv. Mat. Univ. Parma. (IV), 1982, vol. 7, pp. 9–21.

    Google Scholar 

  156. Akinyele, O., Cone-Valued Lyapunov Functions and Stability of Impulsive Control Systems, Nonlin. Anal. TMA, 2000, vol. 39, no.2, pp. 247–259.

    Google Scholar 

  157. Akulenko, L.D., Problems and Methods of Optimal Control, Dordrecht: Kluwer, 1994.

    Google Scholar 

  158. Angeli, D., Ingalls, B., Sontag, E.D., and Wang, Y., Uniform Global Asymptotic Stability of Differential Inclusions, J. Dynam. Control Syst., 2004, vol. 10, no.3, pp. 391–412.

    Google Scholar 

  159. Armellini, G., Sopra Un’equazione Differenziale Della Dinamica, Rend. Acc. Naz. del Lincei, 1935, vol. 21, nos.1–2, pp. 111–116.

    Google Scholar 

  160. Artstein, Z., Stabilization with Relaxed Controls, Nonlin. Anal. TMA, 1983, vol. 7, no.3, pp. 1163–1173.

    Google Scholar 

  161. Avakumovic, V.G., Sur l’Equation Differentielle de Thomas-Fermi, Bull. Inst. Math. Belgrade, 1947, vol. 1, pp. 101–113.

    Google Scholar 

  162. Bajic, V.B., Partial Exponential Stability of Semistate Systems, Int. J. Control, 1986, vol. 44, no.5, pp. 1383–1394.

    Google Scholar 

  163. Bellman, R., Vector Liapunov Functions, SIAM J. Control, Ser. A, 1962, vol. 1, pp. 32–34.

    Google Scholar 

  164. Belloni, M. and Risito, C., On the Global Existence in the Future and Partial Boundedness of Motion of a Wide Class of Holonomic Scleronomic Systems, Rend. Mat. Appl. (VII), 1992, vol. 16, no.4, pp. 587–598.

    Google Scholar 

  165. Benner, P., Partial Stabilization of Generalized State-Space Systems using the Dick Function Method, PAMM, 2003, vol. 2, no.1, pp. 479–480.

    Google Scholar 

  166. Benner, P., Castillo, M., and Quintana-Orti, E.S., Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems, J. Parallel. Distrib. Sci. Eng. Computing, 2004, vol. 1/2.

  167. Benner, P., Castillo, M., Quintana, E.S., and Hernandes, V., Parallel Partial Stabilizing Algorithms for Large Linear Control Systems, J. Supercomput., 2000, vol. 15, no.1, pp. 193–206.

    Google Scholar 

  168. Bernfeld, S.R., Corduneanu, C., and Ignatyev, A.O., On the Stability of Invariant Sets of Functional Differential Equations, Nonlin. Anal. TMA, 2003, vol. 55, nos.4–6, pp. 641–656.

    Google Scholar 

  169. Blanchini, F., Set Invariance in Control, Automatica, 1999, vol. 35, no.11, pp. 1747–1767.

    Google Scholar 

  170. Bondi, P., Fergola, P., Gambardella, L., and Tenneriello, C., Partial Stability of Large-Scale Systems, IEEE Trans. Automat. Control, 1978, vol. 24, no.1, pp. 94–97.

    Google Scholar 

  171. Bondi, P., Fergola, P., Gambardella, L., and Tenneriello, C., Partial Asymptotic Stability via Limiting Equations, Math. Meth. Appl. Sci., 1981, vol. 3, no.4, pp. 516–522.

    Google Scholar 

  172. Brockett, R.W., Asymptotic Stability and Feedback Stabilization: Differential Geometric Control. Theory, Boston: Birkhauser, 1983.

    Google Scholar 

  173. Cai, W.X., The Connective Stability with respect to part of Variables of Dynamic Systems with Delay, J. Xiamen. Univ., Nat. Sci., 1984, vol. 23, no.3, pp. 291–299.

    Google Scholar 

  174. Cai, W.X., The Connective Stability with Respect to Part of Variables of Large-Scale Systems with Delay, J. Xiamen. Univ., Nat. Sci., 1987, vol. 26, no.3, pp. 277–285.

    Google Scholar 

  175. Campanini, R., On the Continuability and Partial Boundedness of the Solutions of Systems of Differential Equations, Bull. Unione Mat. Italy (VI), 1984, vol. 3, pp. 75–84.

    Google Scholar 

  176. Cantarelli, G., Criteria of Partial Boundedness for the Motion of Holonomic Scleronomic Dissipative Systems, Riv. Mat. Univ. Parma (V), 1995, vol. 4, pp. 69–78.

    Google Scholar 

  177. Cantarelli, G., Global Existence and Boundedness for Quasi-Variational Systems, Int. J. Math. Math. Sci., 1999, vol. 22, no.2, pp. 281–311.

    Google Scholar 

  178. Cantarelli, G. and Risito, C., Criteri di Esistenza Globale e di Limitatezza per i Sistemi Olonomi Scleronomi, Ann. Math. Pure Appl. (IV), 1992, vol. 162, pp. 383–394.

    Google Scholar 

  179. Cao, Q.G., Partial Stability of Linear Discrete Systems, J. Math. Res. Expo., 1989, vol. 9, no.4, pp. 541–545.

    Google Scholar 

  180. Cao, Q.G. and Xiong, K.Q., Partial Asymptotic Stability of Linear Time-varying Discrete Systems, Ann. Diff. Equat., 1993, vol. 9, no.2, pp. 141–149.

    Google Scholar 

  181. Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Berlin: Springer-Verlag, 1959.

    Google Scholar 

  182. Chellaboina, V. and Haddad, W.M., Teaching Time-varying Stability Theory using Autonomous Partial Stability Theory, Proc. IEEE Conf. Decision and Control, Orlando, 2001, pp. 3230–3235.

  183. Chellaboina, V. and Haddad, W.M., A Unification between Partial Stability and Stability Theory for Time-varying Systems, IEEE Control Systems Magazine, 2002, vol. 22, no.6, pp. 66–75. (Erratum: IEEE Control Syst. Magazine, 2003, vol. 23, no. 1. pp. 103.)

    Google Scholar 

  184. Corduneanu, C., Sur la stabilite partielle, Rev. Roumaine Math. Pures. Appl., 1964, vol. 9, no.3, pp. 229–236.

    Google Scholar 

  185. Corduneanu, C., Some Problems Concerning Partial Stability, Proc. Symp. Math. Meccanica Non-lineare Stabilita, 1970, New York: Academic, 1971, vol. 6, pp. 141–154.

    Google Scholar 

  186. Corduneanu, C., On Partial Stability of Delay Systems, Ann. Pol. Math., 1974, vol. 29, pp. 357–362.

    Google Scholar 

  187. Djiaferis, T.E., Partial Stability Preserving Maps and Stabilization, Proc. IEEE Conf. Decision Control, 2003, pp. 2490–2495.

  188. Dragan, V. and Halanay, A., Partial Stability for Singularly Perturbed Systems, Proc. Workshop: Diff. Equations and Their Contr., 1983, pp. 36–45.

  189. Edwards, H., Lin, Y., and Wang, Y., On Input-to-State Stability of Time-varying Nonlinear Systems, Proc. IEEE Conf. Decision and Control, Sydney, 2000, pp. 3501–3506.

  190. Efimov, D.V., A Universal Formula for Output Asymptotic Stabilization, Proc. 15 IFAC World Congr., Barselona, Spain, 2002.

  191. El-Gohary, A., Optimal Stabilization of the Rotational Motion of a Rigid Body with the Help of Rotors, Int. J. Nonlin. Mech., 2000, vol. 35, no.3, pp. 393–403.

    Google Scholar 

  192. Esclangon, E., Nouvelles Recherches sur les Fonctions Quasiperiodiques, Ann. Obs. Bordeaux, 1917, vol. 16, pp. 51–226.

    Google Scholar 

  193. Fergola, P. and Moauro, V., On Partial Stability, Ricerche Mat., 1970, vol. 19, no.2, pp. 185–207.

    Google Scholar 

  194. Fergola, P. and Tenneriello, C., Partial Stability of Composite Systems with Unstable Subsystems, Large-Scale Syst., 1983, vol. 4, pp. 101–105.

    Google Scholar 

  195. Fergola, P. and Tenneriello, C., Lotka-Volterra Models: Partial Stability and Partial Ultimate Boundedness, Biomath. Related Comput. Probl., 1988, pp. 283–294.

  196. Fradkov, A.L., Exploring Nonlinearity by Feedback, Physica D, 1999, vol. 128, nos.2–4, pp. 159–168.

    Google Scholar 

  197. Fradkov, A.L., Physics and Control: Exploring Physical Systems by Feedback, Prep. V IFAC Symp. Nonlinear Control Systems, 2001, vol. 5, pp. 1503–1509.

    Google Scholar 

  198. Fradkov, A.L., Miroshnik, I.V., and Nikiforov, V.O., Nonlinear and Adaptive Control of Complex Systems, Dordrecht: Kluwer, 1999.

    Google Scholar 

  199. Fradkov, A.L. and Pogromsky, A.Yu., Introduction to Control of Oscillations and Chaos, Singapure: World Scientific, 1998.

    Google Scholar 

  200. Ge, Z.M. and Chen, Y.S., Synchronization of Undirectional Coupled Chaotic Systems via Partial Stability, Chaos, Solitons, and Fractals, 2004, vol. 21, no.1, pp. 101–111.

    Google Scholar 

  201. Geluk, J.L., Note on a Theorem of Avakumovic, Proc. Am.Math. Soc., 1991, vol. 112, no.2, pp. 429–431.

    Google Scholar 

  202. Guo, Y.X., Partial Stability for Nonlinear Time-varying Dynamical Systems, Ann. Diff. Equat., 1992, vol. 8, no.3, pp. 276–283.

    Google Scholar 

  203. Haddad, W.M., Chellaboina, V., and Nersesov, S.G., A Unification between Partial Stability of State-dependent Impulsive Systems and Stability Theory for Time-dependent Impulsive Systems, Int. J. Hybrid Syst., 2002, vol. 2, nos.1–2, pp. 155–168.

    Google Scholar 

  204. Haddad, W.M., Chellaboina, V., and Nersesov, S.G., A Unification between Partial stability of State-dependent Impulsive Systems and Stability Theory for Time-dependent Impulsive Systems, Proc. Am. Control Conf., Denver, 2003, pp. 4004–4009.

  205. Haddad, W.M., Chellaboina, V., and Oh, J.H., Linear Controller Analysis and Design for Systems with Input Hysteresis and Nonlinearities, J. Franklin Inst., 2003, vol. 340, no.5, pp. 371–390.

    Google Scholar 

  206. Hagedorn, P., Steady Motions in Controlled Gyrostat Systems, Ing. Arch., 1982, vol. 52, no.2, pp. 183–204.

    Google Scholar 

  207. Hahn, W., Stability of Motion, Berlin: Springer-Verlag, 1967.

    Google Scholar 

  208. Halanay, A., Differential Equations: Stability, Oscillations, Time Lags, New York: Academic, 1966.

    Google Scholar 

  209. Hale, J.K., Theory of Functional Differential Equations, New York: Springer-Verlag, 1977. Translated under the title Teoriya funktsional’no-differentsial’nykh uravnenii, Moscow: Mir, 1984.

    Google Scholar 

  210. Hatvani, L., On Partial Asymptotic Stability and Instability. I. Autonomous Systems; II. The Method of Limiting Equations, Acta Sci. Math., 1983, vol. 45, pp. 219–231; vol. 46, pp. 143-156.

    Google Scholar 

  211. Hatvani, L., On the Asymptotic Stability to Nondecreasing Lyapunov Functions, Nonlin. Anal. TMA, 1984, vol. 8, no.1, pp. 67–77.

    Google Scholar 

  212. Hatvani, L., On Partial Asymptotic Stability and Instability. III. Energy-like Ljapunov Functions, Acta Sci. Math., 1985, vol. 49, pp. 157–167.

    Google Scholar 

  213. Hatvani, L., On Partial Asymptotic Stability by the Method of Limiting Equations, Ann. Math. Pura Appl. (IV), 1985, vol. 139, pp. 65–82.

    Google Scholar 

  214. Hatvani, L., On the Stability of the Solutions of Ordinary Differential Equations with Mechanical Applications, Alkalmaz. Mat. Lapok., 1991, vol. 15, no.1/2, pp. 1–90.

    Google Scholar 

  215. Hatvani, L., On the Armellini-Sansone-Tonelli Theorem, Mem. Di_. Equat. Math. Phys., 1997, vol. 12, pp. 76–81.

    Google Scholar 

  216. Hatvani, L. and Terjeki, I., Stability Properties of the Equilibrium under the Influence of Unbounded Damping, Acta Sci. Math., 1985, vol. 48, nos.1–4, pp. 187–200.

    Google Scholar 

  217. Havre, K. and Skogestad, S., Input/output Selection and Partial Control, Proc. 13 IFAC Triennial World Congr., San Francisco, 1996, vol. M, pp. 181–186.

    Google Scholar 

  218. Huang, L., A Discussion on Some Problems of Lyapunov Matrix Equation for Partial Stability, J. Math. Res. Expo., 1990, vol. 10, no.2, pp. 195–198.

    Google Scholar 

  219. Ignatyev, A.O., On the Partial Equiasymptotic Stability of Functional-Differential Equations, J. Math. Anal. Appl., 2002, vol. 268, no.2, pp. 615–628.

    Google Scholar 

  220. Ingalls, B.P., Comparisons of Notions of Stability for Nonlinear Control Systems with Outputs, PhD Dissertation, Rutgers University, New Brunswick, 2001.

    Google Scholar 

  221. Ingalls, B.P., Sontag, E.D., and Wang, Y., Measurement to Error Stability: A Notion of Partial Detectability for Nonlinear Systems, Proc. IEEE Conf. Decision and Control, Las Vegas, 2002, pp. 3946–3951.

  222. Ingalls, B. and Wang, Y., On Input-to-Output Stability for Systems not Uniformly Bounded, Prep. V IFAC Symp. Nonlinear Control Systems, 2001, vol. 5, pp. 1503–1509.

    Google Scholar 

  223. Isidori, A., Nonlinear Control Systems II, London: Springer-Verlag, 1999.

    Google Scholar 

  224. Jian, J.G. and Liao, X.X., Partial Exponential Stability of Nonlinear Time-varying Large-Scale Systems, Nonlin. Anal. TMA, 2004, vol. 59, no.5, pp. 789–800.

    Google Scholar 

  225. Kertesz, V., Partial Stability Investigations of Differential Equational of Second Order, Comput. Math. Appl., 1991, vol. 21, no.1, pp. 95–102.

    Google Scholar 

  226. Khalil, H.K., Nonlinear Systems, Upper Saddle River: Prentice Hall, 1996.

    Google Scholar 

  227. Khapaev, M.M., Usrednenie v teorii ustoichivosti (Averaging in Stability Theory), Moscow: Nauka, 1986.

    Google Scholar 

  228. Kolesnichenko, O. and Shiriaev, A.S., Partial Stabilization of Underactuated Euler-Lagrange Systems via a Class of Feedback Transformations, Syst. Control Lett., 2002, vol. 45, no.2, pp. 299–305.

    Google Scholar 

  229. Kothare, M.V., Shinnar, R., Rinard, I., and Morari, M., On Defining the Partial Control Problem: Concepts and Examples, Proc. Am. Control Conf., Philadelphia, 1998, pp. 2103–2107; AIChE J., 2000, vol. 46, no. 12, pp. 2456-2474.

  230. Kovalev, A.M., Control and Stabilization Problems with Respect to Part of Variables, ZAMM, 1994, vol. 74, no.7, pp. 59–60.

    Google Scholar 

  231. Krichman, M., Sontag, E.D., and Wang, Y., Input-Output-to-State Stability, SIAM J. Contr. Optim., 2000, vol. 39, no.6, pp. 1874–1928.

    Google Scholar 

  232. Krstic, M. and Deng, H., Stabilization of Nonlinear Uncertain Systems, London: Springer-Verlag, 1998.

    Google Scholar 

  233. Kundur, P., Paserba, J., Ajjarapu, V., et al., Definition and Classification of Power Systems Stability, IEEE Trans. Power Systems, 2004, vol. 19, no.3, pp. 1387–1401.

    Google Scholar 

  234. Lakshmikantham, V. and Liu, X.Z., Stability Analysis in Terms of Two Measures, Singapure: World Scientific, 1993.

    Google Scholar 

  235. Lakshmikantham, V. and Salvadori, L., On Massera-type Converse Theorems in Terms of Two Different Measures, Boll. Unione Mat. Ital. Ser. A, 1976, vol. 13, no.2, pp. 293–301.

    Google Scholar 

  236. La Salle, J.P. and Rath, R.J., Eventual Stability, Proc. 2 IFAC Triennial World Congr., 1963, vol. 1, pp. 556–560.

    Google Scholar 

  237. Li, W.J. and Duan, K.C., Partial Stability and Boundedness of Solutions to Retarded Functional-Differential Equations, J. Xinjiang Univ., Nat. Sci., 1993, vol. 10, no.4, pp. 31–33.

    Google Scholar 

  238. Liao, X.X. and Li, J., Robust Interval Stability, Persistence, and Partial Stability on Lotka-Volterra Systems with Time-Delay, Appl. Math. Comput., 1996, vol. 75, nos.2–3, pp. 103–115.

    Google Scholar 

  239. Liao, X.X. and Wu, W.H., Necessary and Sufficient Conditions for the Partial Stability of Linear Dynamical Systems, Chin. Sci. Bull., 1990, vol. 35, no.11, pp. 899–903.

    Google Scholar 

  240. Lin, X.Y., On Converses to the Partial Stability Theorems for Difference Equations, Pure Appl. Math., 1992, vol. 8, no.1, pp. 32–36.

    Google Scholar 

  241. Lin, Y., Lyapunov Functions Techniques for Stabilization, PhD Dissertation, Rutgers University, New Brunswick, 1992.

    Google Scholar 

  242. Lin, Y., Sontag, E.D., and Wang, Y., A Smooth Converse Lyapunov Theorem for Robust Stability, SIAM J. Contr. Optim., 1996, vol. 34, no.1, pp. 124–160.

    Google Scholar 

  243. Luyben, B.L., Tyrens, B.D., and Luyben, M.L., Plantwide Process Control, New York: McGraw-Hill, 1999.

    Google Scholar 

  244. Magnus, K. Kreisel, Theorie und Anwendungen, Berlin: Springer-Verlag, 1971.

    Google Scholar 

  245. Mahony, R., Mareels, I.M., Campion, G., and Bastin, G., Output Stabilization of Square Nonlinear Systems, Automatica, 1997, vol. 33, no.8, pp. 1571–1577.

    Google Scholar 

  246. Mao, X.R., Some Contributions to Stochastic Asymptotic Stability and Boundedness via Multiple Lyapunov Functions, J. Math. Anal. Appl., 2001, vol. 260, no.2, pp. 325–340.

    Google Scholar 

  247. Martynyuk, A.A., Stability by Liapunov’s Matrix Function Method with Applications, New York: Marcel Dekker, 1998.

    Google Scholar 

  248. Meirovitch, L., Liapunov Stability Analysis of Hybrid Dynamical Systems in the Neighbourhood of Nontrivial Equilibrium, Ibid, 1974, vol. 12, no.7, pp. 889–898.

    Google Scholar 

  249. Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability and Boundedness of Discontinuous Dynamical Systems, Nonlin. Studies, 2002, vol. 9, no.3, pp. 225–247.

    Google Scholar 

  250. Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability of Systems with Applications to Discrete Events Systems, Proc. 15 IFAC Triennial World Congr., Barselona, 2002.

  251. Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability of Discontinuous Dynamical Systems, Proc. Am. Contr. Conf., Anchorage, 2002, pp. 74–79.

  252. Michel, A.N., Molchanov, A.P., and Sun, Y., Partial Stability and Boundedness of General Dynamical Systems on Metric Spaces, Nonlin. Anal. TMA, 2003, vol. 52, no.4, pp. 1295–1316.

    Google Scholar 

  253. Michel, A.N. and Sun, Y., Partial Stability of General Dynamical Systems under Arbitrary Initial z-Perturbations, Int. J. Hybrid Syst., 2002, vol. 2, nos.1–2, pp. 57–92.

    Google Scholar 

  254. Miki, K., Partial Integral Stability Theorems by Comparison Principle, Res. Rept. Akita Tech. Coll., 1990, vol. 25, pp. 84–89.

    Google Scholar 

  255. Miki, K., Masamichi, A., and Shoichi, S., On the Partial Total Stability and Partially Total Boundedness of a System of Ordinary Differential Equations, Res. Rept. Akita Tech. Coll., 1985, vol. 20, pp. 105–109.

    Google Scholar 

  256. Miroshnik, I.V., Partial Stability and Geometric Problems of Nonlinear Control, Proc. 15 IFAC Triennial World Congress, Barselona, 2002.

  257. Miroshnik, I.V., Attractors and Partial Stability of Nonlinear Dynamical Systems, Automatica, 2004, vol. 40, no.3, pp. 473–480.

    Google Scholar 

  258. Molchanov, A.P., Michel, A.N., and Sun, Y., Converse Theorems of the Principal Lyapunov Results for Partial Stability of General Dynamical Systems on a Metric Space, Nonlin. Stud., 2003, vol. 10, no.2, pp. 113–134.

    Google Scholar 

  259. Muller, P.S., Stabilitat und Matrizen, Berlin: Springer-Verlag, 1977.

    Google Scholar 

  260. Muller, P.S., Zum Problem der Partiellen Asymptotichen Stabilitat, Fest. zum 70 Gelebr. von Herrn Prof. Dr. K. Magnus, TU Munchen, 1982, pp. 237–268.

  261. Muller, P.S., Kriterien fur Untersuchung der Partiellen Asymptotischen Stabilitas, ZAMM, 1984, vol. 64, no.4, pp. 71–72.

    Google Scholar 

  262. Muller, P.S., Stability and Optimal Control of Nonlinear Descriptor Systems: A Survey, Int. J. Appl. Math. Comput. Sci., 1998, vol. 8, no.2, pp. 269–286.

    Google Scholar 

  263. Muresan, M., On Partial Stability of Differential Inclusions, Proc. Int. Conf. Diff. Equations, Barcelona, 1991, Perello C., Ed., Singapure: World Scientific, 1993, pp. 778–780.

    Google Scholar 

  264. Pachpatte, B.G., Partial Stability of Solutions of Difference Equations, Proc. Nat. Acad. Sci., India, Sect. A, 1973, vol. A3, pp. 235–238.

    Google Scholar 

  265. Pascal, M., La Stabilite d’Attitude dun Satellite muni de Panneaux Solares, Ibid, 1978, vol. 5, no.10, pp. 817–844.

    Google Scholar 

  266. Peiffer, K., La Methode de Liapunoff Appliquée á I Edúte de la StabilitePartielle, Université Catholique de Louvain, Faculté des sciences. 1968.

  267. Peiffer, K. and Rouche, N., Lyapounov’s Second Method applied to Partial Stability, J. Mecanique, 1969, vol. 8, no.2, pp. 323–334.

    Google Scholar 

  268. Peng, L.P., Strong Stability to Part of Variables in Systems with Impulse Effect, J. Beijing Univ. Aeron. Astron., 2001, vol. 27, no.3, pp. 365–369.

    Google Scholar 

  269. Peng, S.T. and Chen, C.K., Estimation of the Partial Stability Region of a Class of Robust Controllers with Input Constraints, J. Franklin Inst., 1998, vol. 335, no.7, pp. 1271–1281.

    Google Scholar 

  270. Phillis, Y., Y-Stability and Stabilizability in the Mean of Discrete-Time Stochastic Systems, Int. J. Control, 1984, vol. 40, no.1, pp. 149–160.

    Google Scholar 

  271. Pico-Marco, E. and Pico, J., Partial Stability for Specific Growth Rate Control in Biotechnological Feed-Batch Processes, Proc. IEEE Conf. Control Appl., 2003, pp. 724–728.

  272. Potcovaru, G., On the Partial Stability of Dynamical Systems with Random Parameters, Ann. Univ. Bucur. Math., 1999, vol. 48, no.2, pp. 163–168.

    Google Scholar 

  273. Prodi, G., Un’ Osservazione Sugl’ Integrali Dell’ Equazione ÿ + A(x)y = 0 Net Caso A(x) → + ∞ per x → + ∞, Rend. Acc. Naz. del Lincei, 1950, vol. 8, pp. 462–464.

    Google Scholar 

  274. Risito, C., Sulla Stabilita Asintotica Parziale, Ann. Math. Pura Appl., 1970, vol. 84, pp. 279–292.

    Google Scholar 

  275. Risito, C., Metodi per lo Studio Della Stabilita di Sistemi con Integrali Primi Noti, Ann. Math. Pura Appl., 1976, vol. 107, pp. 49–94.

    Google Scholar 

  276. Rokni Lamooki, G.R. and Townley, S.B., Partial Stability in Back-Stepping and Adaptive Control, Proc. Int. Conf. Methods Models in Autom. and Robotics, Miedzyzdroje, 2003, pp. 491–496.

  277. Rouche, N., Habets, P., and LaLoy, M., Stability Theory by Liapunov’s Direct Method, NewYork: Springer-Verlag, 1977. Translated under the title Pryamoi metod Lyapunova v teorii ustoichivosti, Moscow: Mir, 1980.

    Google Scholar 

  278. Rouche, N. and Peiffer, K., Le Theoreme de Lagrange-Dirichle et la Deuxieme Methode de Lyapunoff, Ann. Soc. Scient. Bruxelle. Ser. I, 1967, vol. 81, no.1, pp. 19–33.

    Google Scholar 

  279. Routh, J.E., A Treatise on the Stability of a Given State of Motion, London: Macmillan, 1877.

    Google Scholar 

  280. Rumyantsev, V.V., On the Stability to Part of Variables, Symp. Math. Meccanica Nonlineare Stability, New York: Academic, 1971, vol. 6, pp. 243–265.

    Google Scholar 

  281. Russinov, I.K., Partial Asymptotic Stability and Instability of Nonautonomous Systems, Nauchni Tr., Plovdivski Univ. Mat., 1988, vol. 26, no.3, pp. 67–73.

    Google Scholar 

  282. Russinov, I.K., Integral Stability to Part of Variables and Perturbing Lyapunov Functions, Nauchni Tr., Plovdivski Univ., Mat., 1994, vol. 31, no.3, pp. 83–87.

    Google Scholar 

  283. Salvadori, L., Sul Problema Della Stabilita Asimptotica, Rend. Acc. Naz. del Lincei, 1972, vol. 53, nos.1–2, pp. 35–38.

    Google Scholar 

  284. Salvadori, L., Some Contributions to Asymptotic Stability Theory, Ann. Soc. Scient. Bruxelle. Ser. 1, 1974, vol. 88, no.2, pp. 183–194.

    Google Scholar 

  285. Sansone, G., Sopra il Comportamento Asintotico delle Soluzioni di un’ Equazione Differenziale della Dinamica, Scritti Math. offerti a Luigi Berzolari, Pavia, 1936, pp. 385–403.

  286. Sansone, G., Equazioni Differenziali nel Campo Reale, Bologna: Zanichelli, 1949.

    Google Scholar 

  287. Scott, F.J., New Partial Asymptotic Stability Results for Nonlinear Ordinary Differential Equations, Pacific J. Math., 1977, vol. 72, no.2, pp. 523–535.

    Google Scholar 

  288. Scott, F.J., On a Partial Asymptotic Stability Theorem of Willett and Wong, J. Math. Anal. Appl., 1978, vol. 63, no.2, pp. 416–420.

    Google Scholar 

  289. Sepulchre, R., Jankovic, M., and Kokotovic, P.V., Constructive Nonlinear Control, London: Springer-Verlag, 1997.

    Google Scholar 

  290. Shen, J.H. and Du, X.T., Partial Exponential Stability of Large-Scale Nonautonomous Discrete Systems, Acta Sci. Nat. Univ. Norm. Hunan., 1995, vol. 18, no.3, pp. 16–21.

    Google Scholar 

  291. Shen, Y.Y., Partial Stability and Unstability of Ito Stochastic Systems, J. Stangdong Coll. Oceanol., 1982, vol. 12, no.4, pp. 69–76.

    Google Scholar 

  292. Shiriaev, A.S., The Notion of V-Detectability and Stabilization of Invariant Sets of Nonlinear Systems, Syst. Control Lett., 2000, vol. 39, no.5, pp. 327–338.

    Google Scholar 

  293. Shiriaev, A.S. and Fradkov, A.L., Stabilization of Invariant Sets of Cascaded Nonlinear Systems, Proc. IEEE Conf. Decision Control, Phoenix, 1999, pp. 1296–1301.

  294. Shiriaev, A.S. and Fradkov, A.L., Stabilization of Invariant Sets of Nonlinear Nonaffine Systems, Automatica, 2000, vol. 36, no.11, pp. 1709–1715.

    Google Scholar 

  295. Shiriaev, A.S. and Fradkov, A.L., Stabilization of Invariant Sets of Nonlinear Systems with Applications to Control of Oscillations, Int. J. Robust Nonlin. Control, 2001, vol. 11, no.3, pp. 215–240.

    Google Scholar 

  296. Shoichi, S., On the Partial Uniformly Integral Stability of Solutions of Ordinary Differential Equations, Res. Rept. Akita Tech. Coll., 1990, vol. 25, pp. 78–83.

    Google Scholar 

  297. Shoichi, S., Miki, K., and Masamichi, A., Partial Stability Theorems by Comparison Principle, Res. Rept. Akita Tech. Coll., 1982, vol. 17, pp. 95–99.

    Google Scholar 

  298. Shu, W.H., On Partial Stability of Functional-Differential Equations with Delay, J. Cent. China Norm. Univ., Nat. Sci., 1996, vol. 30, no.2, pp. 135–138.

    Google Scholar 

  299. Simenov, P.S. and Bainov, D.D., Stability to Part of Variables in Systems with Impulse Effect, J. Math. Anal. Appl., 1986, vol. 117, no.1, pp. 247–263; 1987, vol. 124, no. 2, pp. 547-560.

    Google Scholar 

  300. Sontag, E.D., A Universal Construction of Artstein’s Theorem on Nonlinear Stabilization, Syst. Control Lett., 1989, vol. 13, no.2, pp. 117–123.

    Google Scholar 

  301. Sontag, E.D., Mathematical Control Theory: Deterministic Finite Dimensional Systems, NewYork: Springer-Verlag, 1998.

    Google Scholar 

  302. Sontag, E.D., The ISS philosophy as a Unifying Framework for Stability Behavior, in Nonlinear Control in The Year Isidori, A., Lamnabhi-Lagarrigue, F., and Respondek, W., Eds., Berlin: Springer-Verlag, 2000, vol. 2, pp. 443–468.

    Google Scholar 

  303. Sontag, E.D., Input-to-State Stability and Related Notions, Proc. Symp. Chemical Process Contr. VI, Tueson, 2001, pp. 109–120.

  304. Sontag, E.D. and Wang, Y., A Notion of Input-to-Output Stability, Proc. Europ. Control Conf., Brussels, 1997, Paper WE-E-A2.

  305. Sontag, E.D. and Wang, Y., Output-to-State Stability and Detectability of Nonlinear Systems, Syst. Control Lett., 1997, vol. 29, nos.4–5, pp. 279–290.

    Google Scholar 

  306. Sontag, E.D. and Wang, Y., Notions of Input-to-Output Stability, Syst. Control Lett., 1999, vol. 38, nos.4–5, pp. 235–248.

    Google Scholar 

  307. Sontag, E.D. and Wang, Y., Lyapunov Characterizations of Input-to-Output Stability, SIAM J. Control Optim., 2001, vol. 39, no.1, pp. 226–249.

    Google Scholar 

  308. Sun, Y. and Michel, A.N., Partial Stability of General Dynamical Systems under Arbitrary Initial z-Perturbations, Tranc. IEEE Conf. Decision Control, Las Vegas, Nevada, 2002, pp. 2663–2668.

  309. Sun, Y. and Michel, A.N., Partial Stability and Boundedness of Discontinuous Dynamical Systems under Arbitrary Initial z-Perturbations, Int. J. Hybrid Syst., 2002, vol. 2, no.3, pp. 261–288.

    Google Scholar 

  310. Sun, Y., Molchanov, A.P., and Michel, A.N., Partial Stability of Dynamical Systems, Proc. 15 Int. Symp. Math. Theory Networks Syst., Univ. Notre Dame, 2002.

  311. Talpalary, P. and Stefancu, D., On Partial Stability of Multivalued Differential Equations, Bull. Inst. Politech. Iasi. Ser. I, 1987, vol. 33, nos.1–4, pp. 41–46.

    Google Scholar 

  312. Tang, S.Y. and Xi, Y.N., Robust Interval Stability and Partial Stability of Kolmogorov Systems with Time Delay, J. Math., Wuhan Univ., 2000, vol. 20, no.2, pp. 180–184.

    Google Scholar 

  313. Teel, A. and Praly, L., A Smooth Lyapunov Function from a Class of K L-estimates Involving Two Positive Semidefinite Functions, ESAIM: Contr., Optimiz. Calculus Variat., 2000, vol. 5, pp. 313–367.

    Google Scholar 

  314. Tian, X.G., An Extension of a Stability Theorem on Discrete Systems and the Lyapunov Function to Partial Stability, Acta Math. Sin., 1993, vol. 36, no.5, pp. 676–681.

    Google Scholar 

  315. Tonelli, L., Estratto di Lettera al Prof. G. Sansone, Scritti Math. offerti a Luigi Berzolari, Pavia, 1936, pp. 404–405.

  316. Tsiotras, P. and Schleicher, A., Detumbling and Partial Attitude Stabilization of a Rigid Spacecraft under Actuator Failure, AIAA Guidance, Navigat. Control Conf., Denver, Colorado, 2000, AIAA Paper 00-4044.

  317. Tsiotras, P. and Wilson, B.C., Zero-and Low-Bias Control Design for Active Magnetic Bearings, IEEE Tranc. Cont rol Syst. Tech., 2003, vol. 11, no.6, pp. 889–904.

    Google Scholar 

  318. Vannelli, A. and Vidyasagar, M., Theory of Partial Stability: Theorems, Converse Theorems, and Maximal Lyapunov Functions, Proc. Annual Southeast Symp., Piscataway, 1980, pp. 16–20.

  319. Vorotnikov, V.I., Ustoi’chivost’ dinamicheskikh sistem po otnosheniyu k chasti peremennykh (Stability of Dynamic Systems Relative to Part of Variables), Moscow: Nauka, 1991.

    Google Scholar 

  320. Vorotnikov, V.I., Partial Stability, Stabilization, and Control: Some Recent results, Proc. 15 IFAC Triennial World Congr., Barselona, 2002.

  321. Wada, T., Ohta, Y., Ikeda, M., and Siljak, D.D., Parametric Absolute Stability of Lur’e Systems, Proc. IEEE Conf. Decision Control, New Orleans, 1995, p. 1449–1454.

  322. Wang, P.K.C., Stability Analysis of Elastic and Aeroelastic Systems via Lyapunov’s Direct Method, J. Franklin Inst., 1966, vol. 281, no.1, pp. 51–72.

    Google Scholar 

  323. Weiss, L. and Infante, E.F., Finite-Time Stability under Perturbing Forces and on Product Spaces, IEEE Tranc. Autom. Control, 1967, vol. 12, no.1, pp. 54–59.

    Google Scholar 

  324. Willems, J.L., A Partial Stability Approach to the Problem of Transient Power System Stability, Int. J. Control, 1974, vol. 19, no.1, pp. 1–14.

    Google Scholar 

  325. Wilson, F.W., Jr., Smoothing Derivatives of Functions and Applications, Trans. Amer. Math. Soc., 1969, vol. 139, pp. 413–428.

    Google Scholar 

  326. Wiman, A., Ueber eine Stabilitatsfrage in der Theorie der linearen Differentialgleichungen, Acta Math., 1936, vol. 66, pp. 121–145.

    Google Scholar 

  327. Wu, C.W. and Chua, L.O., A Unified Framework for Synchronization and Control of Dynamical Systems, Int. J. Bifurcat. Chaos, 1994, vol. 4, no.4, pp. 979–998.

    Google Scholar 

  328. Xiao, H.M. and Liu, Y.Q., Partial Exponential Stability of Large-Scale Systems, Math. Appl., 1990, vol. 3, no.2, pp. 65–70.

    Google Scholar 

  329. Xiao, H.M., Liu, Y.P., and Hu, Y.M., The Partial Boundedness of Neutral Functional Systems and Their Perturbation Systems, Adv. Model. Simul., 1992, vol. 30, no.2, pp. 5–15.

    Google Scholar 

  330. Xiong, K.Q. and Cao, Q.G., On the Partial Stability of a Linear System and Control System, Ann. Diff. Equat., 1989, vol. 5, no.1, pp. 87–97.

    Google Scholar 

  331. Yang, T., Impulsive Control Theory, Berlin: Springer-Verlag, 2001.

    Google Scholar 

  332. Yoshizawa, T., Stability Theory by Liapounov’s Second Method, Tokyo: Math. Soc. Japan, 1966.

    Google Scholar 

  333. Yu, G.D., On the Partial Stability of Impulsive Differential Equations, Ann. Diff. Equat., 1998, vol. 14, no.2, pp. 407–412.

    Google Scholar 

  334. Zames, G., On the Input-Output Stability of Time-varying Nonlinear Feedback Systems. I, II, IEEE Trans. Automat Control, 1966, vol. 11, no.2, pp. 228–238; no. 3, pp. 465-477.

    Google Scholar 

  335. Zhao, J.X., On Partial Asymptotic Stability and Limit Equations, J. Nanjing Univ. Math. Biquart., 1990, vol. 7, no.1, pp. 100–108.

    Google Scholar 

  336. Zhu, H.P. and Mei, F.X., On the Stability of Nonholonomic Mechanical Systems to Part of Variables, Chin. J. Appl. Math. Mech., 1995, vol. 16, no.3, pp. 225–233.

    Google Scholar 

  337. Zubov, S.V., Rated Stability, Proc. 1 Int. Conf. Controlled Oscillations and Chaos, St.-Petersburg, 1997, vol. 1, pp. 170–171.

    Google Scholar 

  338. Zuyev, A.L., On Brockett’s Condition for Smooth Stabilization by Part of Variables, Proc. Eur. Control Conf., Karlsruhe, 1999.

  339. Zuyev, A.L., On Partial Stabilization of Nonlinear Autonomous Systems: Sufficient Conditions and Examples, Proc. Eur. Control Conf., Porte, 2001. pp. 1918–1922.

  340. Zuyev, A.L., Partial Stabilization of a Rigid Body by Several Elastic Beams, Proc. 15 IFAC Triennial World Congr., Barselona, 2002.

  341. Zuyev, A.L., Partial Asymptotic Stability and Stabilization of Nonlinear Abstract Differential Equations, Proc. IEEE Conf. Decision Control, Maui, 2003, pp. 1321–1326.

  342. Zuyev, A.L., On Partial Stabilization of a System of Euler-Bernoulli Beam Equations, The Abdus Salam Int. Center for Theor. Phys., Trieste, 2003.

  343. Zuyev, A.L., On Partial Asymptotic Stabilization of Nonlinear Distributed-Parameter Systems, Automatica, 2005, vol. 41, no.1, pp. 1–10.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural State Technical University, Institute of Technology, Nizhni Tagil, Russia

    V. I. Vorotnikov

Authors
  1. V. I. Vorotnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Avtomatika i Telemekhanika, No. 4, 2005, pp. 3–59.

Original Russian Text Copyright © 2005 by Vorotnikov.

The extended and revised version of this analytical review was supported by the Russian Foundation for Basic Research, project no. 03-01-07003.

This paper was recommended for publication by L.Yu. Rapoport, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vorotnikov, V.I. Partial stability and control: The state-of-the-art and development prospects. Autom Remote Control 66, 511–561 (2005). https://doi.org/10.1007/s10513-005-0099-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10513-005-0099-9

Keywords

Search

Navigation