Sufficient Conditions of Interval Stability of a Class of Linear Impulsive Systems with a Delay

摘要

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.