Research On Stability For Several Classes Of Switched Nonlinear Systems

Switched systems are very important and have their own special laws of hybrid systems. They have the relatively simple structure for us to do the analysis, and they have the practical application. They are an important simplified model of hybrid systems. Switched systems are composed of a set of continuous-time subsystems and the switched rules which determine how to switch between the subsystems. Since switched systems have an increasingly influence and play a significant role in our daily life, more and more scientists focus on it. Theoretical results of switched linear systems have been more abundant, this article will focus on the study of switched nonlinear systems.With a lot of literature and books researched, based on the combination of a common Lyapunov function method, a single Lyapunov function method and multiple Lyapunov function method, according to the characteristics of switched nonlinear systems, the author studied the asymptotic stability and quadratic stability for several classes of switched nonlinear systems.The main contributions of this thesis can be summarized as follows:1. We discuss the global asymptotic stability for a class of switched nonlinear systems, and we use different methods to stabilize the systems in two preconditions. First, we discuss how to construct a common Lyapunov function of the system and how to design the feedback controller to make the system globally asymptotically stable under arbitrary switching in the condition of the zero dynamics of the systems are unstable and the nonlinear partial feedback is stable; and then we consider how to design the switch signals to make the system asymptotically stable with the single Lyapunov function method when the non-linear part isn't the feedback stable, but non-linear convex combination of some of the feedback system is stable.2. We study the global quadratic stability of a class of zero dynamics with quadratic stability of switched nonlinear systems under arbitrary switching. We construct a common Lyapunov function successfully and design a nonlinear state feedback controller for the system to make the system quadratic stability under arbitrary switching. We further study how to use the same coordinate transformation technology to make the system keep quadratic stability under arbitrary switching when its zero dynamics are not quadratically stable.3. We design an appropriate switching signals for a class of switched nonlinear systems whose zero dynamics does not possess the quadratic stability but its convex combination is quadratically stable, and we use multiple Lyapunov function method to ensure the quadratic stability of the system,then we use the same coordinate transformation technology to discuss a more extensive discussion of the situation.Finally, we review the whole dissertation, and discuss the further researching.