Estimating the domains of attraction (DOA) and designing the controller of nonlinear switched systems are important subjects of control theory. In many engineering fields, for the work in security, we must know the DOA of the systems. Switched systems arise in many engineering applications, for example, in motor engine control, robotics control, and networked systems, etc. Meanwhile, research results of switched systems also make significant reference to general hybrid systems in terms of ideas, methods and theories. Therefore, the study of switched systems has great academic value and significant applications.This paper based on sum-of-squares optimization method studies two problems, including estimating the DOA and designing the controller, for a class of nonlinear switched systems under arbitrary switching laws. And it gives two algorithms, estimating the DOA and designing the controller. The main contributions are as follows:(1) Based on sum-of-squares optimization method, it gives an algorithm to estimate the DOA of a class of nonlinear switched systems under arbitrary switching laws. Through the algorithm, we not only find the common Lyapunov function, but also obtain the DOA of the nonlinear switched systems under arbitrary switching laws. After finding the common Lyapunov function, if the initial value is contained in the DOA, the switched systems is asymptotically stable for any switching signals.(2) Based on sum-of-squares optimization method, it gives an algorithm to design the state feedback controller of a class of nonlinear switched systems under arbitrary switching laws. Through the algorithm, we not only find the common Lyapunov function, but also obtain the state feedback controller of the nonlinear switched systems under arbitrary switching laws.Concluding remarks are presented at the end of this article. Some interesting problems are also pointed out, which deserve further study. |