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Construction of Lyapunov functions by the method of localization of invariant compact sets

  • Ordinary Differential Equations
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Abstract

We suggest a new method for constructing Lyapunov functions for autonomous systems of differential equations. The method is based on the construction of a family of sets whose boundaries have the properties typical of the level surfaces of Lyapunov functions. These sets are found by the method of localization of invariant compact sets. For the resulting Lyapunov function and its derivative, we find analytical expressions via the localizing functions occurring in the specification of the above-mentioned sets. An example of a system with a degenerate equilibrium is considered.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, 105005, Russia

    A. P. Krishchenko

  2. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, 119333, Russia

    A. P. Krishchenko

Authors
  1. A. P. Krishchenko
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Correspondence to A. P. Krishchenko.

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Original Russian Text © A.P. Krishchenko, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 11, pp. 1447–1452.

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Krishchenko, A.P. Construction of Lyapunov functions by the method of localization of invariant compact sets. Diff Equat 53, 1413–1418 (2017). https://doi.org/10.1134/S0012266117110039

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  • DOI: https://doi.org/10.1134/S0012266117110039

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