[en] 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. (paper)