Input-to-state Stability Of Runge-kutta Methods For Impulsive Control Systems

Impulsive differential systems can well reflect the instantaneous impact on state, which are widely applied in control systems, ecosystems, economic sys-terns, and aerospace technology and so on, the research of its theory and nu-merical methods is of great importance. For the impulsive control systems, the stability study of analytical solution and numerical methods are important, but fewer papers about numerical method. This paper focuses on studied the input-to-state stability (ISS) of the analytical solution and numerical methods (Runge-Kutta methods) of the impulsive control systems. The main work is as follows:The first chapter describes the application backgrounds and research status of input-to-state stability of impulsive control systems.The second chapter studies the input-to-state stability of the linear impul-sive control systems. And get the ISS conditions of the linear systems and its numerical method (Runge-Kutta methods). The numerical experiment results verify the accuracy of the results.The third chapter studies the input-to-state stability of the nonlinear im-pulsive control systems. And get the ISS conditions of the nonlinear systems and its numerical method (Runge-Kutta methods). The numerical experiment results verify the correctly of the results.