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Mat. Sb., 2019, Volume 210, Number 11, Pages 3–23 (Mi msb9154)  

Sufficient conditions for the stability of linear periodic impulsive differential equations

V. O. Bivziuka, V. I. Slyn'kobc

a 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.

Funding Agency Grant Number
Ministry of Education and Science of Ukraine 0116U004691
National Academy of Sciences of Ukraine 6541230
This study was supported in part by the Ministry of Education and Science of Ukraine (project no. 0116U004691) and the National Academy of Sciences of Ukraine (budget program with budget classification code no. 6541230 “Support for the development of priority areas of scientific research”).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9154

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

Bibliographic databases:

UDC: 517.925.51
MSC: Primary 93D20; Secondary 34A37, 93B12, 93D30
Received: 30.07.2018 and 25.01.2019

Citation: V. O. Bivziuk, V. I. Slyn'ko, “Sufficient conditions for the stability of linear periodic impulsive differential equations”, Mat. Sb., 210:11 (2019), 3–23; Sb. Math., 210:11 (2019), 1511–1530

Citation in format AMSBIB
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\pages 1511--1530
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