Practical Stability Of Impulsive Differential Systems

The research of impulsive differential systems begins in the 1960s. Impulsive differential systems which have vital theoretical significance and practical value, have been involved in many fields, such as information sciences, control systems, life sciences and so on. In this dissertation, different approaches, such as Lyapunov functions including partial components, vector Lyapunov functions, several Lyapunov functions, comparison principle and so on, are employed to study the practical 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 at home and abroad are introduced, and some fundamental symbols and concepts are also given.In the second chapter, the practical stability of impulsive functional differential equations in terms of two measures is studied by using Lyapunov functions including partial components with Razumikhin technique, and one example is given to illustrate the efficiency of the results.In the third chapter, by using a new comparison principle and vector Lyapunov functions 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 an example is given to illustrate efficiency of the result.In the fourth chapter,first,by the comparison method, the eventual practical stability of impulsive differential hybrid systems in terms of two measures is investigated.Second,impulsive differential hybrid systems is investigated by using Lyapunov functions and two examples are given to illustrate the results.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.