Soviet Applied Mechanics

, Volume 17, Issue 10, pp 859–873 | Cite as

Practical stability and stabilization of control processes

  • A. A. Martynyuk
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Keywords

Control Process Practical Stability 

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Literature Cited

  1. 1.
    N. V. Azbelev and Z. B. Tsalyuk, “Integral inequalities. I,” Mat. Sb., No. 56, 325–342 (1962).Google Scholar
  2. 2.
    Dan-Chi Van and S. Ya. Stepanov, “Numerical construction of Lyapunov functions on a finite interval,” in: Problems of Analytical Mechanics, Stability Theory, and Control Theory [in Russian], Nauka, Moscow (1975), pp. 83–90.Google Scholar
  3. 3.
    V. I. Zubov, Stability of Control Processes [in Russian], Sudostroenie, Leningrad (1980).Google Scholar
  4. 4.
    R. E. Kalman, P. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, New York (1969).Google Scholar
  5. 5.
    K. A. Karacharov and A. G. Pilyutik, Introduction to the Engineering Theory of Stability of Motion [in Russian], GFML, Moscow (1963).Google Scholar
  6. 6.
    N. N. Krasovskii, “Appendix IV,” in: I. G. Malkin, Theory of the Stability of Motion [in Russian], Nauka, Moscow (1968).Google Scholar
  7. 7.
    N. N. Krasovskii, Certain Problems in the Theory of the Stability of Motion [in Russian], Fizmatgiz, Moscow (1959).Google Scholar
  8. 8.
    N. N. Krasovskii, Theory of the Stability of Motion [in Russian], Nauka, Moscow (1968).Google Scholar
  9. 9.
    V. I. Kosolapov, “Stability of Motion in the neutral case,” Dokl. Akad. Nauk UzbSSR, Ser. A, No. 1, 27–31 (n. d.).Google Scholar
  10. 10.
    J. P. La Salle and S. Lefschetz, Stability by Liapunov's Direct Method, with Applications, Academic Press, New York (1961).Google Scholar
  11. 11.
    E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York-London (1967).Google Scholar
  12. 12.
    A. M. Lyapunov, General Problem of the Control of Motion [in Russian], ONTI, Moscow-Leningrad (1935).Google Scholar
  13. 13.
    V. M. Matrosov, L. Yu. Anapol'skii, and S. N. Vasil'ev, The Comparison Method in Mathematical Systems Theory [in Russian], Nauka, Novosibirsk (1980).Google Scholar
  14. 14.
    A. A. Martynyuk, “The method of averaging and the comparison principle in the engineering theory of the stability of motion,” Prikl. Mekh.,7, No. 9, 64–69 (1971).Google Scholar
  15. 15.
    A. A. Martynyuk, Engineering Stability in Dynamics [in Russian], Tekhnika, Kiev (1973).Google Scholar
  16. 16.
    A. A. Martynyuk, “Engineering stabilization of controlled motions,” Mat. Fiz., No. 24, 22–27 (1980).Google Scholar
  17. 17.
    A. A. Martynyuk and R. Gutovski, Integral Inequalities and Stability of Motion [in Russian], Naukova Dumka, Kiev (1979).Google Scholar
  18. 18.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).Google Scholar
  19. 19.
    G. I. Mel'nikov, “Aspects of the direct method of Lyapunov,” Dokl. Akad. Nauk SSSR,110, No. 3, 326–329 (1956).Google Scholar
  20. 20.
    S. M. Moldabaev, “Optimal stabilization of nonlinear systems,” in: Dynamics of Controlled Systems [in Russian], Nauka, Novosibirsk (1979), pp. 192–198.Google Scholar
  21. 21.
    E. L. Tonkov, “Problems in the control of periodic motions,” in: Dynamics of Controlled Systems [in Russian], Nauka, Novosibirsk (1979), pp. 286–293.Google Scholar
  22. 22.
    M. M. Khapaev and A. I. Falin, “Stability analysis in systems of integrodifferential equations by the averaging method,” Dokl. Akad. Nauk SSSR,250, No. 2, 295–299 (1980).Google Scholar
  23. 23.
    S. A. Chaplygin, “A new method of approximate integration of differential equations,” in: Selected Works [in Russian], Moscow (1976), pp. 307–360.Google Scholar
  24. 24.
    N. G. Chetaev, “On a notion of Poincare,” in: Collected Scientific Papers of the Aeronautical Institute [in Russian], No. 3, Kazan (1935), pp. 3–6.Google Scholar
  25. 25.
    N. G. Chetaev, “Problems associated with stability of nonsteady motions,” Prikl. Mat. Mekh.,24, No. 1, 6–19 (1960).Google Scholar
  26. 26.
    W. Bogush, Statecznosc Techniczna, PWN, Warsaw (1972).Google Scholar
  27. 27.
    L. T. Grujic, “On practical stability,” Int. J. Control,17, No. 4, 881–887 (1973).Google Scholar
  28. 28.
    V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Vol. 1, Academic Press, New York-London (1969).Google Scholar
  29. 29.
    A. N. Michel and D. W. Porter, “Practical stability and finite-time stability of discontinuous systems,” IEEE Trans. Circuit Theory, CT-19, No. 2, 123–129 (1972).Google Scholar
  30. 30.
    C. P. Tsokos and Mohano Rao Rama, “Finite-time stability of control systems and integral inequalities,” Bul. Inst. Politeh. Iasi,15, Nos. 1–2, 105–112 (1969).Google Scholar
  31. 31.
    L. Weiss and E. F. Infante, “On the stability of systems defined over a time interval,” Proc. Natl. Acad. Sci. USA,54, No. 1, 44–48 (1965).Google Scholar

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© Plenum Publishing Corporation 1982

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  • A. A. Martynyuk

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