Pulse Phenomena And Stability Of Impulsive Control Systems With State-dependent Impulses

Impulsive systems are a kind of mathematical models which describe the phenomenon of abrupt changes in their states with the process of their development.With the rapid development of science and technology,the important theory of impulsive systems and their application value in practice are becoming more and more prominent.However,the impulsive systems with pulse phenomena are more realistic in practical problems,so how to control the pulse phenomenon of impulsive systems with state-dependent impulses is of great practical significance.Based on the theory of impulsive systems,impulsive control systems are developed.Impulsive control is simple,low cost,fast response and low energy consumption.Furthermore,the stability is the primary characteristic of these systems.Therefore,the research of the stability of the impulsive control systems has become a hot issue in international control fields today.This paper mainly deals with pulse phenomena and the stability of impulsive control systems with state-dependent impulses.It mainly includes:In Chapter 1,the research background and meaning of this article,and some former results are introduced.In Chapter 2,it is concerned with pulse phenomena of impulsive systems with state-dependent impulses.Some sufficient conditions which guarantee the absence or presence of pulse phenomena are derived.The results extend and improve those given in some earlier references.Two examples are given to illustrate the efficiency of the obtained results.In Chapter3,based on linear decomposition methods,we derive some sufficient conditions for asymptotic stability and exponential stability of impulsive control systems with state-dependent impulses,and the superiority of the results is evidenced by one example.In Chapter 4,by establishing the concepts of reduced systems and quasistability,the stability problem of a nontrivial solution of the impulsive delay systems with state-dependent impulses is converted to that of the trivial solution of the impulsive delay systems with fixed impulses.We obtain some quasi-stability results of a nontrivial solution of the impulsive delay systems with state-dependent impulses by using some known results for systems with fixed impulses.