Stability Analysis Of Switched Systems

Hybrid dynamic systems are those where the behavior of interest is determined by interacting continuous and discrete dynamics. Continuous dynamics may be considered as the continuous variables while the discrete ones may be considered as versatile incidents, such as sampled-data, logic switching, transformation of system structure and shift of balance point, et, al. The systems are different from single continuous systems or discrete ones in that their systems description is comparatively complicate and more precisely and reasonably depict the problem in the real world.Switched systems are one of the important classes of hybrid dynamic systems, which consist of a family of continuous-time subsystems and a rule that orchestrates the switching between them to achieve the expected performance. Switched systems are widely used in many practical problems, such as switching control of multiple work modes of planes, web switching of electric systems and sampled-data control systems, et, al. The nature of switched systems is switching, however it is not the simple addition of those of different subsystems and has some particularity and complexity. Therefore, the investigation of switched systems is very necessary and has important significance in theory and practice. This dissertation mainly discusses the exponential stability of switched systems and the sufficient conditions of exponential stability are presented.This dissertation is organized as follows:In Chapter 1, we briefly review the history and background of hybrid dynamic systems and switched systems. The methods and techniques used in studying switched systems are introduced and the recent development of switched systems is also presented in this part.The constitution of mathematie model of switched systems is studied in Chapter 2. Firstly, the models of externally forced switching and internally forced switching are founded respectively and two examples are given to explain them. Then, we combine them together to get a uniform model of switched systems and compare with the model of hybrid dynamic systems to show it applicability.In Chapter 3, the exponential stability of switched nonlinear systems is studied. In first, we introduce the method of multiple Lyapunov functions and preceding theory results, and compare with them. In second, using this method, we discuss the exponential stability of switched nonlinear systems and give the sufficient conditions of stability; Furthermore, exponential stability of a class of switched systems with uncertainty is investigated. Mean while, we may translate theorem test into the LMIs problem. In the end, simulation examples are given to show the validity of the result.In Chapter 4, using the vector projection theory, the exponential stability of switched systems is investigated. Firstly, we introduce the vector projection theory and preceding theory results. Secondly, the sufficient conditions of stability linear switched systems are presented; Furthermore, the sufficient conditions of stability of nonlinear switched systems are extended under some conditions. Meanwhile, we design a kind of switching law based on the conditions. Finally, simulation examples are given to show the validity of the result.In the end, there are summary and prospect.