Nonlinear Uncertain Switched System Is Based On The Stability Of The Observer

Hybrid system is a typical complex system, which consists of both continuous variables and discrete variables. It is closely related to many engineering problems. While a switched system which consists of some switching models is a kind of simpler but important hybrid systems. It contacts continuous states with logic states by virtue of switching. With its own particularity, it is different from the traditional continuous time systems or discrete time systems. For example, the difference of switching signals will make stability of systems change and dynamical characteristics complicated. During the last three decades of so, there was an increasing interest on the modeling, analysis, synthesis and control of switched systems.This dissertation devotes on the study of nonlinear switched systems with or without uncertainties, including the design of observers and the switching signals, the globally asymptotical stability and the quadratic stability of the closed-loop systems. The main contents of this paper are as follows:Firstly, we introduce some concepts and mathematical models of switched systems, and review the latest developments of switched systems. Also, we present the theory of Lyapunov stability and some preliminary knowledge.Secondly, the problem of observer design for Lipschitz switched nonlinear systems is considered. By proposing a proper switching strategy and utilizing Schur complement formula and the related notion of LMI, we design a quadratically stable observer which can be used for both finite and infinite switched nonlinear systems. The main result is given in the form of linear matrix inequality. Simulations validate the correctness of the presented algorithms. The simplicity of the design algorithm makes it easy to be carried out.Thirdly, the stabilization problem for nonlinear switched systems with Lipschitz nonlinearity and uncertainty is considered. We analysis the stability of switched systems by considering the local characteristics of the Lyapunov function. Based on the sliding mode observer design and proper switching signals,the matching condition yields a sufficient condition to ensure the stability of the switched error systems via multiple Lyapunov function.At last, it contains a conclusion with discussions on some problems and directions for future study.