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Robust \( H_{\infty } \) Fault-Tolerant Control for Discrete-Time Nonlinear System with Actuator Faults and Time-Varying Delays Using Nonlinear T–S Fuzzy Models

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Abstract

In this paper, the problem of fault estimation and fault-tolerant control for a class of nonlinear discrete-time system state time-varying delay and actuator fault is investigated. This class of systems is represented through the Takagi–Sugeno (T–S) fuzzy model with nonlinear functions satisfying some sector-bounded conditions. By adding these nonlinear functions in the local sub-models, the observer and controller can be designed with fewer rules and less computation burden. The method proceeds in two steps: first, a full-order fuzzy fault estimation observer (FFEO) design is proposed to estimate the actuator faults and the nonlinear functions in the T–S models. Second, based on the online fault estimation, a dynamic output feedback fault-tolerant controller (DOFTC) is then designed to compensate the effect of faults by stabilizing the closed-loop system. Furthermore, sufficient less conservative delay-dependent conditions for the existence of the desired FFEO and DOFTC are given in terms of linear matrix inequalities by employing the fuzzy Lyapunov–Krasovskii function and free-weighting approach. Finally, a practical example is given to show the effectiveness and advantages of the proposed approach.

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Authors and Affiliations

  1. Department of Electronics, Frères Mentouri University, Constantine City, Algeria

    Djamel Eddine Cheridi & Noura Mansouri

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  1. Djamel Eddine Cheridi
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  2. Noura Mansouri
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Correspondence to Djamel Eddine Cheridi.

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Cheridi, D.E., Mansouri, N. Robust \( H_{\infty } \) Fault-Tolerant Control for Discrete-Time Nonlinear System with Actuator Faults and Time-Varying Delays Using Nonlinear T–S Fuzzy Models. Circuits Syst Signal Process 39, 175–198 (2020). https://doi.org/10.1007/s00034-019-01190-2

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