Stability And Robust Stabilization Of Switched Systems

With the development of science and technology and the advancement of our society, many complex systems appear in various fields including traffic transportation, aviation scheduling, engineering technology, etc. These systems usually contain both continuous dynamics and discrete dynamics, and thus are called hybrid dynamical systems. Compared with the general systems, hybrid dynamic systems are able to describe the control problems in actuality more accurate and reasonable. A switched system is one of the important types of hybrid systems, which consists of a family of continuous-time subsystems and a rule that orchestrates the switching between them. Switched systems are widely used in many practice problems, such as computer disc drivers, constrained robotic systems, industrial process control and intelligent vehicle highway systems, etc.Study on hybrid dynamical systems and applications have been developing so quickly in recent years. Especially, the rapid progress in computer science makes it possible to realize hybrid control in practice. As an important class of hybrid systems, switched systems have attracted even more attention in control area because of their extensive background. Compared with common continuous or discrete systems, switched systems possess some special properties. Up to now, the interaction between continuous dynamics and discrete dynamics has not been well understood. Also, there is a lack of effective tools to study switched systems. Therefore, the study of switched systems is usually very difficult and there are many challenging problems that need to be solved.This dissertation studies stability for switched systems and robust stabilization. By using the Lyapunov methods, together with the design of the switching laws, the robust feedback stabilization of switched nonlinear with disturbance and uncertainty simultaneously is discussed. Simulation results are given to show the validity of every result.The dissertation is organized as follows:In chapter 1, the background of task and the recent developments of switched systems are given. The application background of the switched systems is illustrated by a real example. The main work of this dissertation is briefly summarized also.In chapter 2, the structure and basic characteristic of switched systems are given. The characteristic of switched systems is illustrated by some real examples.In chapter 3, the ways to study stability of switched system are given simply.In chapter4, the robust stabilization of a class of switched nonlinear systems with disturbance and uncertainty simultaneously is considered. That system's nominal systems have a common Lyapunov function. A condition to guarantee robust stabilization and the method about how to design a controller are given. We design a controller that can guarantee that the states of the systems are asymptotically stable.