This paper addresses the problems of robust fault estimation and fault-tolerant control for Takagi-Sugeno (T-S) fuzzy systems with time delays and unknown sensor faults. A fuzzy augmented state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Furthermore, based on the information of on-line fault estimates, an observer-based dynamic output feedback fault-tolerant controller is developed to compensate for the effect of faults by stabilizing the resulting closed-loop system. Sufficient conditions for the existence of both a state observer and a fault-tolerant controller are given in terms of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the proposed approach.

The controller synthesis problem for discrete-time positive switched T-S fuzzy systems (PSTSFSs) is investigated in this paper. Unlike previous literature, subsystems are assumed to be partially controllable in this paper. A novel slow-fast combined mode-dependent average dwell time (SFCMDADT) approach is proposed to obtain sufficient conditions for the stability of general positive switched nonlinear systems with partially stable subsystems. Then based on the obtained results, a parallel distributed compensation (PDC)-based fuzzy controller is designed, and sufficient conditions for the stability of PSTSFSs with partially controllable subsystems are developed with the aid of a time-scheduled multiple linear copositive Lyapunov function. Furthermore, sufficient conditions for the stability of the positive switched T-S fuzzy system are given respectively for the two cases that the subsystems are all controllable and all uncontrollable.Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.

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