Global Exponential Stability of Impulsive Delay Systems With Flexible Impulse Frequency

Abstract

We establish global exponential stability theorems for impulsive delay differential systems with flexible impulse frequency. Since impulses often occur instantaneously, intermittently, or irregularly, it is possible that impulses occur with high frequency in some time-domains, and with low frequency in some others, which means that it is not always reasonable for existing results to make assumptions on common lower (or upper) bound of impulsive intervals in the analysis of stability. We propose a new approach which is based on impulsive control theory, the method of auxiliary functions, and linear matrix inequality technique to solve the problem of flexible impulse frequency. This paper mainly focuses on the stability analysis from the impulsive perturbations point of view, that is, the system subjects to destabilizing impulses. In this category, our developing results admit the existence of irregular impulsive intervals. It shows a fact that even there are some time intervals with high impulse frequency, the stability of delay system can still be guaranteed provided that the impulsive intervals with low impulse frequency satisfy certain conditions. Two numerical examples and their simulations are given to show the effectiveness of the proposed approach.