Globally exponential stability of delayed impulsive functional differential systems with impulse time windows

Abstract

In the practical application of impulsive differential systems, impulse does not always occur at the fixed-time point; it may occur in a little range of time. Namely, impulse occurs in a time window, which is more general and more nearing to reality than those fixed-time impulses. Therefore, it is necessary to investigate the dynamical behaviors of impulsive differential systems with impulse time windows. In this paper, the exponential stability of these systems is researched. By means of Lyapunov functions, Razumikhin technique and other analysis methods, several novel exponential stability criteria for delayed impulsive functional differential equations with impulse time windows are obtained, which are different from the previously published results for fixed-time impulses. What is more, based on the analysis of this paper, it is worth noting that choosing an efficient impulse time window may be easier and more effective than choosing fixed-time impulsive sequences. Finally, three examples and their simulations are provided to illustrate the effectiveness of our results.