Automation and Remote Control

, Volume 62, Issue 9, pp 1397–1406 | Cite as

Stability of Complex Systems in Critical Cases

  • A. Yu. Aleksandrov


The stability of the solutions of nonlinear multiconnected systems is investigated by a method based on the use of the Lyapunov second method. Sufficient conditions for the asymptotic stability of certain classes of complex systems in nonlinear approximation are formulated.


Mechanical Engineer Complex System System Theory Asymptotic Stability Critical Case 
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  1. 1.
    Metod vektornykh funktsii Lyapunova v teorii ustoichivosti (The Method of Vector Lyapunov Functions in Stability Theory), Voronov, A.A. and Matrosov, V.M., Eds., Moscow: Nauka, 1987.Google Scholar
  2. 2.
    Gruiich, L.T., Martunyuk, A.A., and Ribbens-Pavella, M., Ustoichivost' krupnomasshtabnykh sistem pri strukturnykh i singulyarnykh vozmushcheniyakh (Stability of Large-Scale Systems under Structural and Singular Perturbations), Kiev: Naukova Dumka, 1984.Google Scholar
  3. 3.
    Rouche, N., Habets, P., and Laloy, M., Stability Theory by Liapunov's Direct Method, New York: Springer-Verlag, 1977. Translated under the title Pryamoi metod Lyapunova v teorii ustoichivosti, Moscow: Mir, 1980.Google Scholar
  4. 4.
    Siljak, D.D., Large-Scale Dynamic Systems: Stability and Structure, New York: North Holland, 1978.Google Scholar
  5. 5.
    Ostrovskii, G.M. and Volin, Yu.M., Metody optimizatsii slozhnykh khimiko-tekhnologicheskikh skhem (Optimization Methods for Complex Chemical Technological Schemes), Moscow: Khimiya, 1970.Google Scholar
  6. 6.
    Voronov, A.A., Ustoichivost', upravlyaemost', nablyudaemost' (Stability, Controllability, and Observability), Moscow: Nauka, 1979.Google Scholar
  7. 7.
    Malkin, I.G., Teoriya ustoichivosti dvizheniya (Theory of Stability of Motion), Moscow: Gostekhizdat, 1952.Google Scholar
  8. 8.
    Krasovskii, N.N., Stability in the First Approximation, Prikl. Mat. Mekh., 1955, vol. 19, issue 5, pp. 516-530.Google Scholar
  9. 9.
    Zubov, V.I., Matematicheskie metody issledovaniya sistem avtomaticheskogo regulirovaniya (Mathematical Methods of Investigating Automatic Regulation Systems), Leningrad: Sudpromgiz, 1959.Google Scholar
  10. 10.
    Kosov, A.A., Stability of Complex Systems in Nonlinear Approximation, Differ. Uravnen., 1997, vol. 33, no. 10, pp. 1432-1434.Google Scholar
  11. 11.
    Aleksandrov, A.Yu., Asymptotic Stability of the Solutions of Systems of Nonstationary Differential Equations with a Homogeneous Right Side, Dokl. Ross. Akad. Nauk, 1996, vol. 349, no. 3, pp. 295-296.Google Scholar
  12. 12.
    Aleksandrov, A.Yu., Asymptotic Stability of the Solutions of Nonlinear Nonautonomous Systems, Izv. Ross. Akad. Nauk., Teor. Sist. Upravlen., 1999, no. 2, pp. 5-9.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • A. Yu. Aleksandrov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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