A Novel Approach to Observer-Based Fault Estimation and Fault-Tolerant Controller Design for T–S Fuzzy Systems With Multiple Time Delays

摘要

In this paper, fault estimation (FE) and fault-tolerant control (FTC) are investigated for Takagi–Sugeno (T–S) fuzzy systems with multiple time-varying delays as well as actuator and sensor faults. Local nonlinear models and external disturbances are also considered. Inspired by the information from the $(k-1)$th induction FE, a novel observer is addressed to establish the $k$th error dynamics. The $k$-step induction FE observer can weaken the effect from input disturbances caused by the derivatives of actuator faults and can perform better FE subject to sensor and actuator faults and multiple time delays simultaneously. Compared with the existing results, the proposed observer can realistically better show the sizes and shapes of the actuator and sensor faults. In addition, according to online information from the $k$-step FE, an active dynamic output feedback fault-tolerant controller is proposed to make the closed-loop fuzzy system asymptotically stable. Moreover, the fuzzy Lyapunov–Krasovskii functional is developed by introducing some free-weighting matrices such that the delay dependent sufficient conditions are given in the form of a set of linear matrix inequalities (LMIs) with less conservatism for the existence of observer and fault-tolerant controller. At last, two simulation examples are given to prove the advantages and effectiveness of the approach given in this paper.