Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency

Abstract

• Stability of impulsive systems with infinite distributed delay is studied via flexible impulse frequency. • The proposed results can be applied to engineering systems with irregular impulses. • A relationship between high impulse frequency and low impulse frequency is established. This paper investigates the global exponential stability of impulsive systems with infinite distributed delay. By introducing two auxiliary functions and two essential lemmas, some sufficient conditions of stability are presented based on flexible impulse frequency, where impulses are considered as perturbations. When the interval between two consecutive impulse times is very small in some time domains, our result just asks that it meets our proposed conditions, which is different from some exist results. The effectiveness of our result is demonstrated through Two simulation examples.