Input-to-state Stability And Stabilization Of Discrete-Time Nonlinear Systems

In recent years,with the rapid development of computer technology,the research of nonlinear discrete systems is particularly important.Input to state stability as a branch of robust control,there have good effects to analysis nonlinear systems with the external disturbance input,so the input-to-state stability has become a common analysis method of nonlinear systems.The theory of input-to-state stability has been involved in many fields of theoretical research and engineering background,such as robot control systems,some engineering systems,biological systems,smart highways,etc.In this paper,we mainly studied the stability of several classes of nonlinear systems with certain conditions and the input to state stabilization problem of a class of nonlinear systems.(1)For a class of discrete-time nonlinear cascade systems,by using the method of Lyapunov function,we will prove that the cascade system composed of integral input-to-state stability subsystems(iISS)is still iISS and give the sufficient conditions on iISS of discrete time cascade systems.Especially,for linear discrete time cascade systems,the sufficient conditions on iISS are provided.Finally,corresponding examples are provided to illustrate the effectiveness of our results.(2)For a class of discrete time switched nonlinear systems,firstly,under the condition of non-switching we will investigate the globally asymptotical stablility(GAS)and input-to-state stability(ISS)of discrete-time nonlinear systems.Then,by using multiple Lyapunov function method and combining with comparison theorem,some sufficient criteria on GAS and ISS are provided for discrete-time switched nonlinear systems.By the average dwell-time method,a sufficient condition on ISS is also obtained.Finally corresponding example is provided to illustrate the effectiveness of our results.(3)For a class of discrete-time nonlinear strict feedback system with external disturbances,through the backstepping design method,we will design the input-to-state stabilization controller for the discrete-time strict feedback systems with external disturbances.Using the theory of Lyapunov function method,the closed-loop system is proved to be ISS.Finally,the numerical simulation illustrates the correctness of our control algorithm.