Stability Of Impulsive Delay Difference Systems

This thesis is composed of three chapters, which mainly studied the stabil-ity of linear impulsive delay difference systems and nonlinear impulsive delay difference systems.As the introductions, in Chapter 1, the background and history of stability for impulsive delay difference systems are briefly addressed, and the main work of this paper is given.In Chapter 2, we studied the stability of linear impulsive delay difference systems. There are 4 sections, the first and the second respectively depict Introduction and Preliminaries. The rest is the main results.In Section 3, we studied the uniformly asymptotic stable and quasi-exponential stable of the linear impulsive delay difference system By using the method of variation of parameters and inequalities, we estab-lished several criteria for uniform asymptotic stability and uniformly quasi-exponential stability of linear impulsive delay difference systems.In Section 4, we studied the uniformly asymptotic stable and quasi-exponential stable of the difference system with time delay in its impulses.In Chapter 3, we studied the stability of nonlinear impulsive delay differ-ence systems. There are 5 sections in chapter 3.In Section 2, we studied the uniformly asymptotic stable and quasi-exponential sable of the nonlinear impulsive delay difference system. By using the method of variation of parameters and inequalities, By using Lyapunov method, we obtain several criteria for uniform asymptotic stability and uniformly quasi-exponential stability of linear discrete impulsive delay system.In Section 3, we studied the uniformly asymptotic stable and quasi-exponential sable of the nonlinear difference impulsive delay system with time delay in its impulses. By using the method of variation of parameters and Lyapunov method, we obtain several criteria for uniform asymptotic stability and uniformly quasi-exponential stability of the nonlinear difference system with time delay in its impulses.In Section 4, we studied the uniformly asymptotic stable and quasi-exponential sable of the nonlinear difference system with time delay in its nonlinear im-pulses. By using the method of variation of parameters, inequalities and Lyapunov method, we obtain several criteria for uniform asymptotic stability and uni-formly quasi-exponential stability of the nonlinear difference system with time delay in its nonlinear impulses.In Section 5, we studied the impulsive synchronization of difference chaotic systems. Master System: Slave System: The error system: By using the result in Theorem and Corollary, we gain the sufficient conditions of difference synchronization.