This article is cited in 7 papers

Sufficient conditions for the stability of linear periodic impulsive differential equations

V. O. Bivziuk^a, V. I. Slyn'ko<sup>bc

a</sup> University of Illinois at Urbana-Champaign, Urbana, IL, USA
^b S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine, Kiev, Ukraine
^c Julius-Maximilians-Universität Würzburg, Würzburg, Germany

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.

Keywords: abstract linear impulsive differential equations, commutator calculus, Lyapunov stability, Lyapunov functions.

UDC: 517.925.51

MSC: Primary 93D20; Secondary 34A37, 93B12, 93D30

Received: 30.07.2018 and 25.01.2019

DOI: 10.4213/sm9154

 English version: Sbornik: Mathematics, 2019, 210:11, 1511–1530

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