The Study Of Stability Of Impulsive Switched Systems On Partial Variables

In this dissertation, the stability of linear impulsive switched systems on partial variables is firstly analyzed by useing interceptive matrix method. Then the stability of nonlinear impulsive switched systems on partial variables is proposed by arbitrary switching method. For the linear impulsive switched systems, Cauchy matrices solutions of systems are used to study its properties on the partial variable of y; for the nonlinear ones, properties on the partial variable of y are studied. The sufficient conditions of the stability on partial variables are given based on Lyapunov functions.At first, definitions and research summarizations of some systems are introduced in this dissertation. The description of the partial variables is also proposed. Research results of their stabilities are intruduced and some deficiency is analyzed. Then, the innovation of this dissertation is presented.Secondly, some methods to analyze the stability on partial variables are proposed. They are Multi-Lyapunov function method, arbitrary switching method, Linear Matrix Inequality (LMI) method, interceptive matrix method, respectively.For linear impulsive switched systems, Cauchy matrix solution is introduced. Properties of partial variables are studied by using interceptive matrix method. The sufficient and necessary conditions of the stability on partial variables are given, including the uniform stability, the asymptotical stability and the exponential stability. In addition, by means of the idea of interceptive matrix method, a conclusion of the asymptotic stability on partial variables is given based on LMI.For nonlinear impulsive switched systems, a suitable Lyapunov function on partial variables is introduced. Applying the method of Multi-Lyapunov function, properties of partial variables under arbitrary switching are researched. The sufficient criterias of the stability on partial variables are given, including the uniformstability, the asymptotical stability, the uniform asymptotical stability and the exponential stability. Some numerical examples are proposed to illustrate the effectiveness of obtained results. The stability of partial variables is discussed by means of Lyapunov first approximation theory. Based on this theory, we transform a class of nonlinear impulsive switched system into linear impulsive switched system.The last section is the conclusions of this dissertation. For both linear and nonlinear impulsive switched systems, some valuable problems of the stability on partial variables are proposed. Meanwhile, the future research target is indicated.