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Sbornik: Mathematics, 2014, Volume 205, Issue 6, Pages 862–891
DOI: https://doi.org/10.1070/SM2014v205n06ABEH004401 (Mi sm8233) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action

A. I. Dvirnyja, V. I. Slyn'kob

a Hedmark University College
b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine
English version PDF (609 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2014v205n06ABEH004401
Abstract: Inverse theorems to Lyapunov's direct method are established for quasihomogeneous systems of differential equations with impulsive action. Conditions for the existence of Lyapunov functions satisfying typical bounds for quasihomogeneous functions are obtained. Using these results, we establish conditions for an equilibrium of a nonlinear system with impulsive action to be stable, using the properties of a quasihomogeneous approximation to the system. The results are illustrated by an example of a large-scale system with homogeneous subsystems.
Bibliography: 30 titles.
Keywords: impulsive action, quasihomogeneous system, Lyapunov stability, Lyapunov's direct method.
Received: 24.03.2013 and 09.12.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 6, Pages 109–138
DOI: https://doi.org/10.4213/sm8233
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
MSC: Primary 35R12; Secondary 34A37
Language: English
Original paper language: Russian
Citation: A. I. Dvirnyj, V. I. Slyn'ko, “Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action”, Mat. Sb., 205:6 (2014), 109–138; Sb. Math., 205:6 (2014), 862–891
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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