Globally exponential stabilization of switched nonlinear systems with arbitrary switchings
Switched nonlinear systems (SNS) are control systems that involve both continuous and discrete dynamics. The design of switched nonlinear systems is mainly composed of two parts. One is to design a smooth controller for each continuous subsystem such that each subsystem satisfies certain given requirements, the other is to define a switching law for the continuous controllers such that the overall switched nonlinear system achieves some given specifications. The continuous controllers, together with the corresponding switching law, form a switched controller. In this paper, we consider the problem of globally exponential stabilization of switched nonlinear systems with arbitrary and infinite number of "switchings". We handle both the case where the switchings of the system coincide exactly with the switchings of the controllers and the case where the switchings of the system do not coincide exactly with the switchings of controllers. An SNS in the first case and in the second case is called a synchronous SNS and an asynchronous SNS, respectively. Methods are presented to design switched controllers in both cases. Some sufficient conditions are derived to globally exponentially stabilize the system in both cases. However, emphasis is placed on the second case.