Switching Time Delay System Stability And Robust H_ ¡Þ Control Problem,

In the natural world and society practice, many objective things' development depend on past behavior or state. This kind of property is called time delay, such as latent period of infectious disease, hysteresis effect of elasticity, time delays of network transmission and queuing. Typical examples include mechanical transmission systems, fluid transmission systems,metallurgical industry processes and network control systems. Time delay is often the reason of instability and chaos. In recent years, many researchers have devoted to study the relevant control problems of time-delay systems. In addition, in recent years, due to the vast application of switched system control, there is an increasing interest on the modeling, analysis, synthesis, and control of switched systems. Nowadays more and more people have paid attention to the stability analysis of the switched systems and the study of the switching control.This dissertation mainly deals with uncertain switched control systems with time delay. By resorting to Lyapunov function, the concept of matrix measure, improved Razumikhintypetheorem, the property of M-matrix, and in combination with the idea of matrix decomposition and integral inequality, the problem of stability and control design are considered.The main contributions of the research work presented in this dissertation are as follows:In Chapter 1, we give a brief review of hybrid dynamical systems and the development of switched systems and time-delay systems. We also summarize the main results of this dissertation.In chapter 2, the stability problem for a class of switched linear systems with time delay is addressed.Based on the Lyapunov function method and the concept of matrix measure, both the timedelayindependent criteria and time-delay dependent criteria for the asymptotic stability and exponential stability are proposed respectively. The corresponding stabilizing switching laws are provided.In chapter 3, we study the following delay-independent stability for the switched timedelaylarge-scale system by employing an improved Razumikhin-type theorem and the M- matrix properties.In chapter 4, the robust H_∞control problem is studied for a class of uncertain linear systems with time delay.By resorting to linear matrix inequality method and the concept of matrix decomposition, a memoryless robust H_∞state feedback controller is given.In chapter 5, we present the conclusion of this dissertation.