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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  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

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© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Alexey A. Ignatyev

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