Design of robust observer-based controller for Time-delay switched fuzzy systems with unmeasurable premise variables

This paper addresses the problem of robust observer-based controller design for the time-delay switched fuzzy systems with unmeasurable premise variables. A switched fuzzy system, which integrates fuzzy and switching features, can describe continuous and discrete modes and complex nonlinear phenomena of objective reality as well as their coupling and interactions. The fuzzy observer with unmeasurable premise variables is designed to estimate the system states. The stability and the switching control law based on measured state of the dynamic errors system are then analyzed by multiple Lyapunov function approach. Then the estimated system states are used for the state-feedback control of switched fuzzy systems. In this study, the robust control problem of an uncertain time-delay switched fuzzy system is solvable, which some sub time-delay fuzzy systems are allowed to be unstable. The robust stability conditions in the form of linear matrix inequalities (LMIs) are derived. Two numerical simulations are provided to show the validity of the proposed method.