A sojourn probability approach to fuzzy-model-based reliable control for switched systems with mode-dependent time-varying delays

Abstract

This paper addresses reliable control design for a switched system (SS) described by T-S fuzzy model subject to actuator failures and mode-dependent time-varying delay. A different type of switching law is introduced with the aid of sojourn probabilities (SPs) technique. The sojourn probability depicts the probability of a switched system staying in subsystem. It should be pointed out that, the SPs describe the probabilities of SSs stay in each subsystems which is easily measured. Both completely known and partly unknown SPs are proposed for the T-S fuzzy SSs. By using a matrix inequality approach and by constructing a proper Lyapunov–Krasovskii functional, less conservatism sufficient conditions are achieved in the form of linear matrix inequalities. A single link robot arm system is given to illustrate the validity of proposed design procedure.