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The direct Lyapunov method for an almost periodic difference system on a compactum

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Abstract

We establish a sufficient condition for asymptotic stability for the systems under consideration in which the condition on the difference derivative by the system is weakened in comparison with the Lyapunov condition \( \dot \nu < 0 \) We also obtain applications to the analysis of stability of equilibria of dynamical systems with infinite-dimensional phase space.

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Authors and Affiliations

  1. Omsk State Technical University, Omsk, Russia

    S. M. Dobrovol’skii

  2. Omsk State Technical University, Omsk, Russia

    A. V. Rogozin

Authors
  1. S. M. Dobrovol’skii
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  2. A. V. Rogozin
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Additional information

Original Russian Text Copyright © 2005 Dobrovol’ski\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) S. M. and Rogozin A. V.

The authors were supported by the Russian Foundation for Basic Research (Grant 01-01-00303).

Translated from Sibirski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 98–105, January–February, 2005.

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Dobrovol’skii, S.M., Rogozin, A.V. The direct Lyapunov method for an almost periodic difference system on a compactum. Sib Math J 46, 77–82 (2005). https://doi.org/10.1007/s11202-005-0008-z

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  • DOI: https://doi.org/10.1007/s11202-005-0008-z

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