On the Stability of Periodic Impulsive Systems

On equiasymptotic stability of solutions of doubly-periodic impulsive systems

“…The stability of solution (3) of the periodic system (1), (2) was studied in [8]. It was shown in [8] that asymptotically stable solutions of periodic systems are uniformly asymptotically stable, and sufficient conditions for their asymptotic stability were obtained. In what follows, we consider system (1), (2) under the assumption that conditions (5) are satisfied and the number ω ω…”

“…This resulted in an increase in the number of works devoted to the investigation of various aspects of the theory of impulsive systems [6 -13]. In the present paper, which is a continuation and development of [8], we study the stability of solutions of impulsive systems.…”

Asymptotic stability and instability with respect to part of variables for solutions to impulsive systems

“…In line with [18,14], we introduce the following definitions: Definition 2.5. We say that a function V :…”

“…The results of the first articles on impulsive differential equations are gathered in the monograph [11] which presents the basics of this theory. Lately, we observe a significant increase of the number of mathematical articles on the various aspects of the theory of impulse systems [12][13][14][15][16][17] which is due to the demands of the modern technology. Simeonov and Bainov [18] stated the stability problem for solutions to impulsive systems with respect to part of variables and proved a series of theorems.…”