Study On Input-to-State Stability Of Nonlinear Impulsive Systems

Impulsive systems have been widely recognized and concerned in control theory,and have been widely used in many physical and biological phenomena.However,it is inevitable that there will exist disturbance inputs in practical application.For this problem,in 1989,Sontag introduced the basic concept of input-to-state stability.This theoretical concept effectively describes the stability characteristics of nonlinear systems with external inputs,and it is one of the important and basic contents of the stability of nonlinear control systems.It is of great practical significance to study the input-to-state stability characteristics of nonlinear impulsive systems and has gradually become the focus of control theory and technology research.The input-to-state stability of nonlinear impulsive systems are mainly discussed in this paper.The main research contents are as follows:The first chapter introduces the research background of this paper,and briefly summarizes the main work of this paper.The second chapter studies the input-to-state stability and integral input-to-state stability of nonlinear systems with hybrid inputs and delayed impulses.According to Lyapunov method,some sufficient conditions for input-to-state stability and integral input-to-state stability are obtained,and the effects of time delay in hybrid impulses,that is,the stabilizing impulses and destabilizing impulses,are further studied.Two numerical examples are given to prove the validity of the conclusion.The third chapter studies the input-to-state stability of the network of nonlinear systems with delayed impulses.Based on the small gain condition,some sufficient conditions for the input-to-state stability of such interconnections are established by using the results obtained in the second chapter.Eventually,a numerical example is provided to illustrate the effectiveness of the results.