Stability Analysis And Robust H_∞ Control For Uncertain Discrete Markov Switched Systems

Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems (or discrete time dynamic systems), which interact on each other. Switched systems are essentially a class of nonlinear systems. It consists of some linear subsystems that integrate the logical and continuous dynamics by switching.Markov switched systems, which describe many engineering and social economics problems, need to be investigated for theoretical significance and engineering value. As a class of hybrid systems, the states are constituted by two parts:the discrete part which describes the mode of the systems and the continuous part which describes the dynamic process of the systems. A large of practical systems have variable structures subject to random changes, which result from the abrupt phenomena such as component and interconnection failure. Systems with this character may be considered as Markov switched systems. Nowadays, more and more people have paid attention to the stability analysis of the Markov switched systems and the study of the robust H∞control.Firstly, this paper introduces background and significance of the Markov switched systems and summarizes basic knowledge of linear matrix inequality and Lyapunov stability. It analyzes the feature of continuous-time and discrete-time Markov switched systems. Secondly, it discusses the stability of the switched systems and uncertain discrete-time switched systems. Meanwhile, it studies the stability and robust H∞control problems of the uncertain discrete-time Markov switched systems. Then it designs memoryless state feedback controllers in terms of linear matrix inequalities. Finally, numerical examples show effectiveness of the proposed methods.