Geodesic
Sufficient conditions for the stability of linear periodic impulsive differential equations
Sbornik. Mathematics, Tome 210 (2019) no. 11, pp. 1511-1530

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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. 
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     author = {V. O. Bivziuk and V. I. Slyn'ko},
     title = {Sufficient conditions for the stability of linear periodic impulsive differential equations},
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V. O. Bivziuk; V. I. Slyn'ko. Sufficient conditions for the stability of linear periodic impulsive differential equations. Sbornik. Mathematics, Tome 210 (2019) no. 11, pp. 1511-1530. http://geodesic.mathdoc.fr/item/SM_2019_210_11_a0/