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Stability of Complex Systems in Critical Cases

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Abstract

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.

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REFERENCES

  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. 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. 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. Siljak, D.D., Large-Scale Dynamic Systems: Stability and Structure, New York: North Holland, 1978.

    Google Scholar 

  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. Voronov, A.A., Ustoichivost', upravlyaemost', nablyudaemost' (Stability, Controllability, and Observability), Moscow: Nauka, 1979.

    Google Scholar 

  7. Malkin, I.G., Teoriya ustoichivosti dvizheniya (Theory of Stability of Motion), Moscow: Gostekhizdat, 1952.

    Google Scholar 

  8. Krasovskii, N.N., Stability in the First Approximation, Prikl. Mat. Mekh., 1955, vol. 19, issue 5, pp. 516-530.

    Google Scholar 

  9. Zubov, V.I., Matematicheskie metody issledovaniya sistem avtomaticheskogo regulirovaniya (Mathematical Methods of Investigating Automatic Regulation Systems), Leningrad: Sudpromgiz, 1959.

    Google Scholar 

  10. Kosov, A.A., Stability of Complex Systems in Nonlinear Approximation, Differ. Uravnen., 1997, vol. 33, no. 10, pp. 1432-1434.

    Google Scholar 

  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. 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.

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Aleksandrov, A.Y. Stability of Complex Systems in Critical Cases. Automation and Remote Control 62, 1397–1406 (2001). https://doi.org/10.1023/A:1011676123661

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