Sufficient conditions for the stability of linear periodic impulsive differential equations

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...

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Bibliographic Details
Published in:Sbornik. Mathematics 2019-11, Vol.210 (11), p.1511-1530
Main Authors: Bivziuk, V. O., Slyn'ko, V. I.
Format: Article
Language:English
Subjects:
abstract linear impulsive differential equations
Asymptotic properties
commutator calculus
Differential equations
Liapunov functions
Lyapunov functions
Lyapunov stability
Mathematical analysis
Stability
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9154