Dependent On The State Of The Stability Of Impulsive Differential Systems

The theory of impulsive differential systems has been involved many fields, for example: dynamics, biology, information sciences, and so on. In this dissertation, Lyapunov functions and comparison principle are employed to study the stability of impulsive differential systems.The dissertation includes five chapters, which is summarized as follows:In the first chapter, the current research situations and developments of impulsive differential systems with variable impulsive perturbations at home and abroad are introduced, and some fundamental symbols and concepts are also given.In the second chapter, by the comparison method, the stability of impulsive differential systems with variable impulses is studied, and one example is given to illustrate the efficiency of the results.In the third chapter, the definitions of practical stability in terms of two measurements for impulsive differential systems with variable impulsive perturbations are given. By using a new comparison principle about impulsive differential systems with variable impulsive perturbations, the practical stability properties in terms of two measurements for impulsive differential systems with variable impulsive perturbations are investigated, and one example is given to illustrate the efficiency of the results.In the fourth chapter, the definitions of eventual practical stability for impulsive differential systems with variable impulsive perturbations are given. By using Lyapunov functions and comparison principle, the eventual practical stability properties in terms of two measurements for impulsive delay differential systems with variable impulsive perturbations are investigated, and by using direct method, the practical stability properties in terms of two measurements for impulsive delay differential systems with variable impulsive perturbations are given.In the fifth chapter, conclusion, the brief summarizes for the above sections are presented, and the outlooks about the issue in this dissertation are developed.