Fault-Tolerant Control for T–S Fuzzy Descriptor Systems with Sensor Faults: An LMI Approach

Abstract

This paper focuses on the robust sensor fault-tolerant control of T–S fuzzy descriptor systems with unmeasurable premise variables subject to external disturbances. By introducing sensor fault as an auxiliary state vector, an augmented fuzzy descriptor system is constructed. A robust fuzzy descriptor observer is investigated to achieve simultaneous reconstruction of system states and sensor faults using descriptor approach and the \(L_2\) techniques to minimize the effect of the perturbations on the state estimation error. Based on the state estimated variables and by isolating the sensor fault, a fault-tolerant control scheme is proposed using a state feedback controller approach such that the resulting closed-loop system is stable with prescribed \(H_{\infty }\) performance. Sufficient conditions for the existence of a robust fuzzy descriptor observer and a fault-tolerant controller are derived in the sense of Lyapunov asymptotic stability and are formulated in terms of a series of linear matrix inequalities without additional constraints. Finally, a numerical example was discussed to prove the performance of the proposed approach.