Stability Analysis and $$H_\infty $$ Performance for Nonlinear Fuzzy Networked Control Systems with Time-Varying Delay

Ech-charqy, Ahmed; Idrissi, Said; Ouahi, Mohamed; Tissir, El Houssaine; Naami, Ghali

doi:10.1007/978-981-15-0947-6_5

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“…Takagi-Sugeno (T-S) systems are a kind of the fuzzy system introduced in Tanaka and Wang (2004) to facilitate the use of fuzzy system tools for some nonlinear systems. Because of the effective representation of a nonlinear system as a set of local linear models that are interpolated by nonlinear functions, T-S fuzzy methods have proved useful in a variety of problems (Ammar et al 2018;Tuan VLB, and Hajjaji 2018;Chaibi et al 2019;Naami et al 2019;Ejegwa 2020;Yang et al 2020;Saif et al 2020;Dutta and Doley 2021;Zhang and Huang 2021;Kchaou and Jerbi 2021;Ech-charqy et al 2020; D'Urso 2017; Najariyan et al 2017). Stability analysis and controller design can then be handled with this technique (Takagi and Sugeno 1985;Tanaka et al 1998) for nonlinear systems (Xie et al (2020)), by an equivalent combination of linear systems.…”

Section: Introductionmentioning

confidence: 99%

Design of robust control for uncertain fuzzy quadruple-tank systems with time-varying delays

et al. 2022

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The robust $$H_\infty$$ H ∞ observer-based control design is addressed here for non-linear Takagi-Sugeno (T-S) fuzzy systems with time-varying delays, subject to uncertainties and external disturbances. This is motivated by the quadruple-tank with time delay control problem. The observer design methodology is based on constructing an appropriate Lyapunov–Krasovskii functional (LKF) for an augmented system formed from the original and the delayed states. The bilinear terms are transferred to the linear matrix inequalities, thanks to a change of variables which can be solved in one step. Furthermore, by employing the $$\mathcal {L}_2$$ L 2 performance index, the adverse effects of persistent bounded disturbances is largely avoided. The proposed method has the advantage of relating the controller and Lyapunov function to both the original and delayed states. Then, the controller and observer gains are obtained simultaneously by solving these inequalities with off-the-shelf software (Yalmip/MATLAB toolbox). Finally, an application to a simulated quadruple-tank system with time delay is carried out to demonstrate the benefits of the proposed technique, showing a compromise between controller simplicity and robustness that outperforms previous approaches.

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