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Robust stability and \({H_\infty }\) control problem for 2-D nonlinear uncertain switched system with mixed time-varying delays under fuzzy rules

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Abstract

In this paper, the robust stability and \({H_\infty }\) control problem of two-dimensional (2-D) nonlinear polytopic uncertain switched system with mixed time-varying delays is studied based on Roesser model, and the nonlinear system is cleverly broken down into linear forms under the Takagi-Sugeno (T-S) fuzzy rules. Assuming its uncertain parameters are given by convex bounded polyhedral domain. First of all, an improved multi-parameter Lyapunov–Krasovskii function (LKF) is proposed to work hard to get additional information related to time delays, so that it is less conservative. Second, using the aforementioned LKF coupled with Finsler’s lemma, finite-sum inequalities, and Jensen inequalities, a new sufficient condition in linear matrix inequalities (LMIs) is derived for robust \({H_\infty }\) performance analysis of 2-D nonlinear polytopic uncertain switched system. Third, for this system with time delays, a memory-state feedback controller including information about the past of the system state is designed to remove the effect of time delays on the system, and the resulting closed-loop system is robustly asymptotically stable under the specified \({H_\infty }\) disturbance attenuation level \(\gamma \). Finally, the superiority and effectiveness of the proposed results are illustrated by simulation examples.

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Acknowledgements

This work was partially supported by Natural Science Foundation of Hebei Province (F2022203085), the S &T Program of Hebei under Grant (F2020203037), Science Fund for Creative Research Groups of Hebei Province (F2020203013), and National Natural Science Foundation of China (618255304).

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  1. School of Science, Yanshan University, Qinhuangdao, 066004, Hebei, People’s Republic of China

    Dan Peng & Mengjie Liu

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  1. Dan Peng
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  2. Mengjie Liu
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Correspondence to Dan Peng.

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This work is supported in part by Natural Science Foundation of Hebei Province F2022203085, S &T Program of Hebei under Grant F2020203037, Science Fund for Creative Research Groups of Hebei Province F2020203013, and National Natural Science Foundation of China 618255304.

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Peng, D., Liu, M. Robust stability and \({H_\infty }\) control problem for 2-D nonlinear uncertain switched system with mixed time-varying delays under fuzzy rules. Comp. Appl. Math. 42, 328 (2023). https://doi.org/10.1007/s40314-023-02440-5

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  • DOI: https://doi.org/10.1007/s40314-023-02440-5

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