The Stability Problems For Some Kinds Of Impulsive Difference Systems

This thesis mainly studies the stability problems for some kinds of delay difference systems with impulsive. It is consisted of four chapters.As the introduction, in Chapter 1, the background and history of impulsive equations and impulsive delay difference systems are briefly addressed, and the research methods of these problems and the main results of this work are stated.In Chapter 2, we study the impulsive stabilization of delay difference equa-tions. There are three sections. The first section is about the Introduction and Preliminaries. The second section is the main results, the third section is about an application of the result. In section 2, we studied the system under the impulsive control x(ηk)=βk(x(ηk-1)), with the stability theorems of functional differential systems with impulses at steady times, and we established a criteria for globally exponentially stability of impulsive delay difference system,and get the related corollary.In Chapter 3, we consider the stability problems of a class of delay difference equations, there are two sections. The first section are about the Introduction and Preliminaries, and some related definitions. The second section is the main result, which discussed the uniformly stability and uniformly asymptotic stability of a class of difference system with the Razumikhin techniques, established the stability criteria of the impulsive delay difference system above.In Chapter 4, we discussed the stability of the impulsive difference delay systems of the three chapter again, there are two sections. The first section is about Introduction and Preliminaries. Similarly with chapter 3, in the second section studied a new Razumikhin-type theorem for impulsive delay difference equations, and studied a new weak exponentially stability of this system.In chapter 5, is the summary of the all article and about the outlook.