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

• Published in: IET control theory & applications Vol. 14; no. 11; pp. 1411 - 1423
• Main Authors: Sun, Shaoxin, Zhang, Huaguang, Cai, Yuliang, Mu, Yunfei
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 23.07.2020
• Subjects: active dynamic output feedback fault tolerant controller design; actuator faults; actuators; adaptive control; closed loop systems; closed‐loop fuzzy system; control system synthesis; delay systems; delay‐dependent sufficient conditions; discrete time systems; discrete‐time multiple state‐delayed T–S fuzzy systems; discrete‐time Takagi–Sugeno fuzzy systems; fault tolerant control; feedback; fuzzy control; fuzzy Lyapunov function; fuzzy systems; linear matrix inequalities; local nonlinear dynamics; Lyapunov methods; multiple time‐varying state delays; nonlinear control systems; nonlinear dynamical systems; novel fuzzy adaptive descriptor observer; n‐step error functions; n‐step induction FE; observers; observer‐based fault estimation; Research Article; sensor; stability; time‐varying systems; uncertain systems; time-varying systems; delay systems; n-step induction FE; fuzzy Lyapunov function; nonlinear dynamical systems; observer-based fault estimation; feedback; fuzzy control; actuators; active dynamic output feedback fault tolerant controller design; linear matrix inequalities; closed-loop fuzzy system; multiple time-varying state delays; n-step error functions; fuzzy systems; stability; local nonlinear dynamics; discrete time systems; actuator faults; uncertain systems; control system synthesis; adaptive control; discrete-time Takagi–Sugeno fuzzy systems; closed loop systems; discrete-time multiple state-delayed T–S fuzzy systems; novel fuzzy adaptive descriptor observer; nonlinear control systems; sensor; delay-dependent sufficient conditions; observers; Lyapunov methods; fault tolerant control
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2019.0690

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.