On Optimal Stabilization of Nonautonomous Systems

  • Alexey A. Ignatyev


Consider a controlled system of differential equations of perturbed motion
$$ \dot x = X(t,x;u), $$
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
$$ t \in R, \left\| x \right\| < H (H = const). $$


Periodic Function Asymptotic Stability Control Function Continuous Dependence Convergent Subsequence 
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    LG. Malkin, The Stability of Motion Theory, Moscow, Nauka, 1966.Google Scholar
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  3. 3.
    A.Ya. Savchenko and A.O. Ignatyev, Some Problems of Stability of Non-autonomous Dynamical Systems, Naukova Dumka, Kiev, 1989.Google Scholar

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© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Alexey A. Ignatyev

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