Switched System Analysis Based On Dwell Time

In this article, our research mainly aims at the switched system as an important class of hybrid dynamical systems, which is composed of a family of continuous-time or discrete-time subsystems and a rule orchestrating the switching among the subsystems. Due to the switching signal, its dynamical performance becomes very complicated. The stability, robustness and disturbance attenuation may change due to the switching law. Hence, it is very important to choose a property switching law.This dissertation investigates how to choose a proper switching law from switching time for the linear switched systems. Using a dwell time or average dwell time approach incorporated with a piecewise Lyapunov function to study the stability and input-to-output L2 gain of the switched systems. The main contributions of the research work presented in this dissertation are as follows:(1)The stability of discrete-time singular linear switched systems with impulsive effects is studied by using dwell time and average dwell time approaches. Sufficient conditions for exponential stability are presented. The validity of the algorithm is illustrated in a numerical example.(2)A converter which is the typical switched system in power electronic system is studied, and the model for the converter is set up. The stability of the system is studied by using dwell time approaches and at the same time considering practical condition to confirm the parameter. The simulation by Matlab is shown.(3)The issue of the L2 gain property for linear impulsive switched systems is addressed. A weighted L2 gain is achieved via piecewise Lyapunov function incorporated with an average dwell time approach. The theorem and its proof are presented. Based on this theory, the L2 gain for discrete-time linear impulsive switched system is also studied and the theorem and its proof are presented too.