H ∞ Fault Estimation and Fault-Tolerant Control for T-S Fuzzy Systems with Actuator and Sensor Faults Using Sliding Mode Observer

Abstract

This paper investigates the problems of the robust fault estimation (FE) and fault-tolerant control (FTC) for the Takagi-Sugeno (T-S) fuzzy systems with unmeasurable premise variables (PVs) subject to external disturbances, actuator, and sensor faults. An adaptive fuzzy sliding mode observer (SMO) with estimated PVs is designed to reconstruct the state, actuator, and sensor faults simultaneously. Compared with the existing results, the proposed observer is with a wider application range since it does not require the knowledge of the upper bound of faults that some FE methods demand. Based on the FE information, a dynamic output-feedback fault-tolerant controller (DOFFTC) is designed to compensate the effect of faults by stabilizing the closed-loop systems. By using the $H_{\infty }$ filtering method, sufficient conditions for the existence of the proposed SMO and DOFFTC are derived in terms of linear matrix inequalities (LMIs) optimization. Finally, a nonlinear inverted pendulum system is given to validate the proposed methods.