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 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.
abstract linear impulsive differential equations, commutator calculus, Lyapunov stability, Lyapunov functions.
|Ministry of Education and Science of Ukraine
|National Academy of Sciences of Ukraine
|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”).
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Sbornik: Mathematics, 2019, 210:11, 1511–1530
MSC: Primary 93D20; Secondary 34A37, 93B12, 93D30
Received: 30.07.2018 and 25.01.2019
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
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\by V.~O.~Bivziuk, V.~I.~Slyn'ko
\paper Sufficient conditions for the stability of linear periodic impulsive differential equations
\jour Mat. Sb.
\jour Sb. Math.
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