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Avtomatika i Telemekhanika, 2017, Issue 6, Pages 36–56 (Mi at14444)  
This article is cited in 10 scientific papers (total in 10 papers)

Nonlinear Systems

Investigation of asymptotic stability of equilibria by localization of the invariant compact sets

A. P. Krishchenko

Bauman Moscow State Technical University, Moscow, Russia
Full-text PDF (1767 kB) Citations (10)
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Abstract: The method of localization of invariant compact sets was proposed to study for asymptotic stability the equilibrium points of an autonomous system of differential equations. This approach relies on the necessary and sufficient conditions for asymptotic stability formulated in terms of positive invariant sets and invariant compact sets, and enables one to study the equilibrium points for asymptotic stability in the cases where it is impossible to use the first approximation or the method of Lyapunov functions. The possibilities of the method were illustrated by examples.
Keywords: equilibrium point, asymptotic stability, invariant compact set, positive invariant set, localizing set.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.4769.2017/ВУ
Russian Foundation for Basic Research 16-07-00902
16-07-00927
This work was supported by the Russian Ministry of Education and Science, project no. 1.4769.2017/VU, and the Russian Foundation for Basic Research, projects nos. 16-07-00902 and 16-07-00927.
Presented by the member of Editorial Board: P. V. Pakshin

Received: 27.04.2016
English version:
Automation and Remote Control, 2017, Volume 78, Issue 6, Pages 989–1005
DOI: https://doi.org/10.1134/S0005117917060030
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. P. Krishchenko, “Investigation of asymptotic stability of equilibria by localization of the invariant compact sets”, Avtomat. i Telemekh., 2017, no. 6, 36–56; Autom. Remote Control, 78:6 (2017), 989–1005
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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