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On Optimal Stabilization of Nonautonomous Systems

  • Alexey A. Ignatyev

Abstract

Consider a controlled system of differential equations of perturbed motion
$$ \dot x = X(t,x;u), $$
(18.1)
where x = (x 1,…, x n), X = (X1,…, X n ), u = (u1,…,u r ). Suppose that functions X(t, x, u) are defined, continuous, and satisfying a Lipschitz condition in x in the domain
$$ t \in R, \left\| x \right\| < H (H = const). $$
(18.2)

Keywords

Periodic Function Asymptotic Stability Control Function Continuous Dependence Convergent Subsequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    LG. Malkin, The Stability of Motion Theory, Moscow, Nauka, 1966.Google Scholar
  2. 2.
    B.M. Levitan and V.V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge University Press, Cambridge, 1982.MATHGoogle Scholar
  3. 3.
    A.Ya. Savchenko and A.O. Ignatyev, Some Problems of Stability of Non-autonomous Dynamical Systems, Naukova Dumka, Kiev, 1989.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Alexey A. Ignatyev

There are no affiliations available

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