Finite-time Stabilization Of A Class Of Switched Systems

With the development of science technology and society, there are many new challenges in modeling and control theory, which includes, for example, a single model cannot describe the dynamic behavior of the system or a single controller cannot achieve the control objective. Therefore, the hybrid system model and switching control technology are put forward and have attracted increasing attention in recent years. As an important class of the hybrid systems,switched system has attracted much more attention.Although lots of results on stabilization of switched nonlinear systems have been obtained during the past two decades, most of the results are asymptotic stabilization. On the other hand, we request the state trajectory to reach equilibrium in finite time in most practical applications. In addition, it is shown that, compared with the asymptotic stabilized systems, the finite-time stabilized systems usually practically demonstrate some desired features such as faster convergence rates, higher accuracies, and better disturbance rejection properties. However,the results of finite-time stabilization for switched nonlinear systems is still very limited. Therefore,this article will study the global finite-time stabilization problem for a class of switched nonlinear systems. The main contents are as follows:The second chapter investigates the finite-time stabilization problem for a class of switched nonlinear systems, whose subsystems have the p-normal form.Unlike the traditional p-normal form whose highest power is odd number, the powers of the studied subsystem in this paper are allowed to be even, which makes the traditional finite-time control design method is no longer work.In this paper, by using the convex combination technique and the adding one power integrator technique, we obtain the sufficient conditions which ensure the global finite-time stabilization for the studied switched nonlinear systems, and realize the co-design of controller and switching law. Finally, an example is presented.The third chapter studies the finite-time control problem for a class of nonlinear systems with chain structure. Based on input-state scaling, the system can be converted to the one in lower triangle structure, and the switching controller is designed with adding one power integrator technique and the switching control method. Then, the finite-time control of the studied system is realized. Compared with the traditional design method,the proposed method has faster convergence speed in this chapter.Finally, the propose method is applied to type unicycle mobile robot.Finally, the full context is summarized in the Chapter four.