H₂/H_? Control For Switched Singular Systems

The switched singular systems is a significant class of hybrid systems, which is composed by a number of subsystems, each subsystem can be arbitrary switch,or be switched by appropriate switch rules. Switch singular system compared with the normal switch systems, its subsystems are normally linear or non-linear singular systems. The theory of normal systems well developed, which greatly contributed to the development of switch singular systems.So,this paper mainly studies the switched singular systems of H2/H? control problem.Based on Lyapunov stability theory of the singular system, taking advantage of advanced multiple Lyapunov function approach, this paper does some research on H2 control and H2/H? control for a class of the switch singular systems respectively, which is involved as follows:(1) Solved H2 state feedback control problems for a class of the switch singular system. Take advantage of multiple Lyapunov function approach, the sufficient conditions of the linear matrix inequalities for the existence of controller and switch law for the switch singular system is proposed, which enables the closed-loop switch singular systems asymptotically stable and satisfies the H2 performance. Numerical examples confirm the correctness of the method.(2) H2/H? state feedback control for a class of the switched singular systems. Based on the theory of linear matrix inequalities, using multiple Lyapunov function approach, for the switch singular systems of the H2/H? state feedback controller and switch rules is designed. The convex optimization problem is established for H2/H? control and its optimization solution is given which has less conservative property then before. Numerical examples confirm the correctness of the method.