Asymptotic Behaviors And Practical Stability Of Delayed Impulsive Differential Systems

In the present thesis, the asymptotic behaviors and practical stability of solutions of delayed impulsive differential systems are discussed. The contents are divided into three sections. In the first part we introduce the background and current situation of research for impulsive differential systems with delay. The definitions and assumptions are also given in this section. In the second part, by using the integral inequality technology, we obtain some criteria of asymptotic behaviors of solutions for the delayed impulsive differential systems And then, the achieved results are applied to investigate the asymptotic behaviors of a class of second order impulsive differential equation In the last part, we consider a special case of delayed impulsive differential systems and, by making use of an approach different from the Lyapunov Function method, obtain two criteria of practical stability, including the finite-time stability and infinite-time stability.