Abstract

A class of linear periodic impulsive systems with a delay is considered. Sufficient conditions of asymptotic stability are established for systems of this class, reducing the study of the original system’s stability to a similar problem for a system of linear impulsive differential equations (without a delay). This auxiliary result is used to study the interval stability of a linear impulsive system with a delay under general assumptions about the dynamic properties of continuous and discrete components. Examples are given to illustrate the effectiveness of the obtained results.

中文翻译：

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一类线性时滞脉冲系统区间稳定性的充分条件。

摘要

考虑一类具有时滞的线性周期脉冲系统。为此类系统建立了充分的渐近稳定性条件，从而将对原始系统稳定性的研究减少到一个线性脉冲微分方程系统（无延迟）的类似问题。该辅助结果用于研究线性脉冲系统的时滞稳定性，该线性时滞系统具有关于连续和离散分量的动力学特性的一般假设。举例说明所获得结果的有效性。