Robust H-infinity Control For Uncertain Switched Systems

Switched systems, an important class of Hybrid Dynamic Systems, have extensive practical background and great significance of theoretical study.Because of switched systems to improve system performance in the role, and its rapid development to meet the needs of intelligent control, switched systems research has made some progress and made some achievements. According to the latest developments of switched systems,the research results of the robust H-infinity control problem for uncertain switched systems are less. So we do some research in this respect in this paper: we put some typical uncertainties into switched systems and discuss the robust H-infinity control problem for uncertain switched systems. The main contents of this paper are as follows:We introduce some background and review on the latest developments of switched systems and robust H-infinity control.Based on multiple Lyapunov function method, the robust H-infinity control problem for uncertain switched linear systems is discussed in this paper. For all admissible uncertainties,the state feedback controllers and switching laws to ensure both the relevant closed-loop systems and the prescribed L2 ?gain from disturbance input to the controlled output are designed respectively. The sufficient condition for the robust H-infinity control problem is derived in this paper. The condition is given in terms of a group of partial differential inequalities which are more solvable than general Hamilton-Jacobi inequalities. Then,as an application,a hybrid state feedback technique to solve the robust H- infinity control problem for non-switched linear systems is presented. This method transforms the H-infinity control problem of general systems into that of a certain switched system and has strong robustness for the variation of system parameters.Then, the results investigated in this paper are applied to the robust H-infinity control problem for uncertain switched nonlinear systems. Research methods, ideas and findings are a similar situation with the linear system. Based on multiple Lyapunov function technique, the robust H-infinity control problem for uncertain switched nonlinear systems which contain uncertainties in the system state, input channel and interference is discussed in this paper. The sufficient condition for the robust H-infinity control problem of the relevant closed-loop systems is derived, because the state feedback controllers and switching laws are designed. The condition is given in terms of a group of partial differential inequalities. Then,as an application,a hybrid state feedback technique to solve the robust H- infinity control problem for non-switched nonlinear systems which contain uncertainties in the system state, input channel and interference is presented.At last,it contains a conclusion with discussions on some problems.