Impact of initial time difference on stability criteria of impulsive differential equations

Abstract

In this paper, an impulsive differential system is investigated for the first time for several stability criteria relative to initial time difference. The investigations are carried out by perturbing Lyapunov functions and by using comparison results. A generalized Lyapunov function has been used for the investigation.The results that are obtained to investigate the stability significantly depend on the moment of impulses. An example is given to illustrate the derived result.