Abstract
We study the problem of μ-stability of a dynamical system with delay. Conditions of the practical μ-stability are established for the general case and for a quasilinear system. The conditions suggested are illustrated by an example.
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Yu. A. Mitropol’skii,Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).
A. N. Filatov,Averaging Methods for Differential and Integro-Differential Equations [in Russian], Fan, Tashkent (1971).
J. La Salle and S. Lefshchetz,Stability by Liapunov’s Direct Method, Academic Press, New York (1961).
A. A. Martynyuk,Practical Stability of Motion [in Russian], Naukova Dumka, Kiev (1983).
V. Lakshmikantham, S. Leela, and A. A. Martynyuk,Stability of Motion: Method of Comparison [in Russian], Naukova Dumka, Kiev (1991).
A. A. Martynyuk, “Stability analysis: nonlinear mechanics equations,” in:Stability and Control: Theory, Methods and Applications, Ser. ISSSN-1023-6155, Gordon Breach, New York (1995).
V. I. Fodchuk, “On the continuous dependence of solutions of delay differential equations on a parameter,”Ukr. Mat. Zh.,16, No. 2, 273–279 (1964).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 204–213, February, 1999.
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Martynyuk, A.A., Chen-Tsi, S. On the practical μ-stability of solutions of standard systems with delay. Ukr Math J 51, 224–236 (1999). https://doi.org/10.1007/BF02513475
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DOI: https://doi.org/10.1007/BF02513475