Fault-tolerant SMC for Takagi–Sugeno fuzzy systems with time-varying delay and actuator saturation

• Published in: IET control theory & applications 2017-05, Vol.11 (8), p.1112-1123
• Main Authors: Selvaraj, Palanisamy, Kaviarasan, Boomipalagan, Sakthivel, Rathinasamy, Karimi, Hamid Reza
• Format: Article
• Language: English
• Subjects: actuator fault matrix; actuator saturation; Actuators; Asymptotic properties; asymptotic stability; closed loop systems; closed‐loop system; control system synthesis; Delay; delay systems; external disturbances; Fault tolerance; fault tolerant control; fault‐tolerant sliding mode control design; fault‐tolerant SMC; fuzzy control; Fuzzy systems; gain matrix; linear matrix inequalities; LMI; Lyapunov methods; Lyapunov stability; passivity; performance constraints; reachability analysis; Saturation; Sliding; sliding surface function; sliding surface reachability; SM surface; Special Issue: Recent Developments on Sliding Mode Control and Its Applications for Complex Systems; sufficient conditions; Surface stability; system trajectories; Takagi–Sugeno fuzzy systems; time‐varying delay; time‐varying systems; variable structure systems
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2016.0845

This study examines the problem of fault-tolerant sliding mode control (SMC) design subject to actuator saturation for a class of Takagi–Sugeno fuzzy systems with time-varying delay and external disturbances. Our main attention is to propose the fault-tolerant SMC such that for given any initial condition, the system trajectories are forced to reach the sliding surface within a finite time. On the basis of the SM surface and Lyapunov stability theorem, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established to not only guarantee the passivity and asymptotically stability of the resulting closed-loop system in the designed sliding surface, but also cover the issues of actuator saturation and performance constraints. Then, the desired gain matrix of the fault-tolerant SMC is obtained in respect of the previously established LMIs such that the reachability of the predefined sliding surface is ensured. It is worth pointing out that the obtained sufficient conditions can preserve the trade-off between the maximisation of admissible upper bound of time-varying delay and enlarging the estimation about the domain of attraction for the closed-loop system. Eventually, the effectiveness and robustness of the proposed control approach are demonstrated via simulation results.