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Asymptotic stability analysis of autonomous systems by applying the method of localization of compact invariant sets

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Abstract

The asymptotic stability and global asymptotic stability of equilibria in autonomous systems of differential equations are analyzed. Conditions for asymptotic stability and global asymptotic stability in terms of compact invariant sets and positively invariant sets are proved. The functional method of localization of compact invariant sets is proposed for verifying the fulfillment of these conditions. Illustrative examples are given.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    A. P. Krishchenko

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

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Original Russian Text © A.P. Krishchenko, 2016, published in Doklady Akademii Nauk, 2016, Vol. 469, No. 1, pp. 17–20.

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Krishchenko, A.P. Asymptotic stability analysis of autonomous systems by applying the method of localization of compact invariant sets. Dokl. Math. 94, 365–368 (2016). https://doi.org/10.1134/S1064562416040025

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  • DOI: https://doi.org/10.1134/S1064562416040025

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