Observer and fault‐tolerant controller design for discrete‐time multiple state‐delayed T–S fuzzy systems

Abstract

This study is concerned with observer-based fault estimation (FE) and fault-tolerant controller design for a class of discrete-time Takagi–Sugeno (T–S) fuzzy systems. There exist multiple time-varying state delays, sensor and actuator faults, local non-linear dynamics and exogenous disturbances in the systems. In comparison with the existing results, the approach suggested in this study is more flexible and feasible. By means of the n-step induction FE, a novel fuzzy adaptive descriptor observer is developed to obtain the n-step error functions. Then, an active dynamic output feedback fault-tolerant controller is designed to stabilise the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function which utilises the form of linear matrix inequalities. The stability results from the observer and the controller in this study have less conservatism compared with the ones from the existence of observers and fault-tolerant controllers. At last, a simulation example is presented to demonstrate the advantages and effectiveness of the approach proposed in the study.