Robust H_∞ Control For Switched Singular Systems

This paper mainly studied two types of switched singular systems with time- delay and uncertainties, the switched continuous singular systems and the switched discrete-time singular systems. Time-delay is a common phenomenon in nature, the change rate of the state in the time-delay systems not only dependent on the current state, but also dependent on the past state; In reality systems, due to inevitable effected by the various external factors, uncertainties widely exist in various systems.The switched singular systems is an important class of hybrid systems, which is composed by a number of subsystems, each subsystem can be arbitrary switching,or be swtched by appropriate switching rules. Switched singular system compared with the normal switched systems, its subsystems are normal linear or non-linear singular systems.The theory of normal systems well developed,which greatly contributed to the development of switched singular systems.Based on Lyapunov stability theory of the singular system, take advantage of advanced multiple Lyapunov function approach,this paper do some research on robust H∞ control problems for the switched continuous singular systems and the switched singular discrete-time systems,which all contained time-delay and uncertainties, the main research work of this paper as follows:(1) Solved H∞ state feedback problems for the the switched continuous singular system with time-delay and uncertainties. Take advantage of the completeness theory, through multiple Lyapunov function approach,the linear matrix inequalities sufficient conditions for existence of robust controller is given, what’s more, designed the controller to satisfy the set requirements-Numerical examples confirmed the correctness of of the method.(2) For switched discrete-time singular systems with time-delay and uncertainties, based on the theory of linear matrix inequalities,using multiple Lyapunov function approach,the H∞ state feedback controller and switching rules is designed for the switched discrete-time singular systems with time-delay and uncertainties,what’s more,a sufficient delay-dependent robust stability condition to satisfy the H∞ performance y is proposed.