Uniformly Asymptotical Stability Of Zero Solution Of Impulsive Differential Equations With Infinite Delay

Consider the following impulsive differential systems with infinite delay :The study of stability is one of basic and important subject in the research of impulsive functional differential equations. In this work, it is considered for the stability of zero solution of impulsive differential equations with infinite delay. By using Lyapunov functionals and the new Razumikhin technique, the uniformly asymptotical stability of zero solution of impulsive differential equations with infinite delay is discussed. Some known results are extended and improved. The new Razumikhintechnique is first established by Shunian Zhang. With the piecewise definition, the structure of Lyapunov function is simpler than before and more general results are obtained, which have strong applicability and operability. An example is introduced at the end of the paper to illustrate the advantage of our results.