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Sbornik: Mathematics, 2019, Volume 210, Issue 11, Pages 1511–1530
DOI: https://doi.org/10.1070/SM9154 (Mi sm9154) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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
English version PDF (542 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM9154
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”).
Received: 30.07.2018 and 25.01.2019
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 11, Pages 3–23
DOI: https://doi.org/10.4213/sm9154
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
MSC: Primary 93D20; Secondary 34A37, 93B12, 93D30
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 7 articles:
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