Adaptive Fuzzy Observer-Based Fault-Tolerant Control for Takagi–Sugeno Descriptor Nonlinear Systems with Time Delay

Abstract

This paper investigates the problems of state/fault estimation and active fault-tolerant control (AFTC) design for time-delay descriptor fuzzy systems subject to external disturbances and actuator faults. Using Takagi–Sugeno fuzzy models, an adaptive fuzzy observer is proposed to achieve system state and actuator fault estimation simultaneously. According to Lyapunov functional method, design and analysis conditions of the resulting closed-loop delayed descriptor system are formulated in terms of linear matrices inequalities (LMIs). Observer and controller gains are computed by solving a set of LMIs in only one step and then used to both estimate the unmeasured states and actuator faults in AFTC context. Numerical examples are provided to show the merit and the conservativeness of the proposed approach in comparison with the existing methods by considering various types of actuator faults.