H∞ control for a class of cascade switched nonlinear systems

Abstract

In this paper, we investigate the H-infinity control problem for a class of cascade switched nonlinear systems consisting of two nonlinear parts which are also switched systems using the multiple Lyapunov function method. Firstly, we design the state feedback controller and the switching law, which guarantees that the corresponding closed-loop system is globally asymptotically stable and has a prescribed H-infinity. performance level. This method is suitable for a case where none of the switched subsystems is asymptotically stable. Then, as an application, we Study the hybrid H-infinity control problem for a class of nonlinear cascade systems. Finally, an example is given to illustrate the feasibility of our results.