Research On Input State Stability Of Several Kinds Of Switching Nonlinear Systems

Switched systems is generally regarded as an important class of hybrid systems, which has a wide range of engineering background and theoretical significance. Switched systems are composed of multiple subsystems and switching rules, which is expanded from the traditional deterministic system state space model. The switched systems are not only successfully used in modeling systems with sudden environmental disturbances, but also improve the control accuracy due to the more detailed description for the actual system. Stability is the basic premise for the study of system performances, and the research on the stability theory appear layer upon layer without end. The input-to-state stability is proposed by Sontag, which can describe the influence of the external input to the system state, and play an important role in the analysis and synthesis of nonlinear systems.The input-to-state stability theory has been widely used in spacecraft attitude control, chemical process analysis and so on. The research on the switching system is based on the Lyapunov stability theory, and the current research methods are based on the traditional negative definite derivative Lyapunov-like function method and the traditional dwell time method, which clearly is conservative in some sense. This paper mainly focuses on the input-to-state stability of several classes of switched nonlinear systems. The main conclusions that we derive are as follows:1) Integral input-to-state stability of switched nonlinear systems with unstable continuous dynamics.This article deals with integral input-to-state stability(iISS) of switched nonlinear systems with unstable continuous dynamics based on a Lyapunov-like function with indefinite derivative.It is not necessarily required that all the subsystems are iISS. A Lyapunov-like function with indefinite derivative is constructed rather than a negative definite derivative one. As a result, new sufficient conditions are established which are proved to be more relaxed than the existing results.An illustrative example is presented to demonstrate the effectiveness of the main results.2) Input-to-state stability of switched nonlinear delay systems based on an average dwell time method.This paper discovers some new sufficient conditions for the input-to-state stability(ISS) of switched nonlinear delay systems. The cases where the switching signal of the system and the switching signal of the corresponding controller are synchronous and asynchronous are both considered. We combine the Lyapunov-Krasovskii functional with indefinite derivative with the merging switching signal technique to guarantee the ISS of the switched nonlinear delay system under the asynchronous switching scheme. Finally, a simulation of a simpler delay model is provided to illustrate the effectiveness of the proposed result.3) Input-to-state stability of discrete-time switched nonlinear systems with adjective modedependent average dwell time.This paper investigates the input-to-state stability of discrete time switched nonlinear systems with adjective mode-dependent average dwell time(AMDADT). The switching with modedependent average dwell time presents a more practical phenomenon, the asynchronous switching into account, where “ asynchronous ” indicates that the switching between the controllers and the system modes are in the presence of a time delay. By combing the asynchronous switching, new sufficient conditions on the input-to-state stability analysis for the systems are first given where the Lyapunov-like functions during the running time of subsystems are allowed to increase. Finally,an example is given to illustrate the effectiveness of the proposed theory.