Sufficient conditions for the stability of linear periodic impulsive differential equations

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Abstract

Abstract linear periodic impulsive differential equations are considered. The impulse effect instants are assumed to satisfy the average dwell-time condition (the ADT condition). The stability problem is reduced to studying the stability of an auxiliary abstract impulsive differential equation. This is a perturbed periodic impulsive differential equation, which considerably simplifies the construction of a Lyapunov function. Sufficient conditions for the asymptotic stability of abstract linear periodic impulsive differential equations are obtained. It is shown that the ADT conditions lead to less conservative dwell-time estimates guaranteeing asymptotic stability. Bibliography: 24 titles.

About the authors

Vladyslav Olegovich Bivziuk

University of Illinois at Urbana-Champaign

Vitalii Ivanovich Slyn'ko

Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine; Julius-Maximilians-Universität Würzburg

Email: vitstab@ukr.net
Doctor of physico-mathematical sciences, Head Scientist Researcher

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