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Robust \({{H}_{\infty }}\) control for uncertain Takagi–Sugeno fuzzy systems with state and input time-varying delays

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Abstract

This paper puts forward an augmented Lyapunov–Krasovskii functional (LKF) method to investigate the robust \({{H}_{\infty }}\) control problem of uncertain Takagi–Sugeno fuzzy systems (TSFSs) with delays which includes delay-product-type terms. On the basis of the new augmented LKF and improved boundary techniques, the sufficient asymptotic stability condition is derived in this paper. And the robust \({{H}_{\infty }}\) controller is further designed, which is able to ensure that the fuzzy time delay system (TDS) has the specified \({{H}_{\infty }}\) performance index. Subsequently, four numerical examples are presented to illustrate the effectiveness and advantage of the put forward methodology.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China No. 61273004, and the Natural Science Foundation of Hebei province No. F2021203061. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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

    Di Mao & Yuechao Ma

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  1. Di Mao
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  2. Yuechao Ma
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Correspondence to Yuechao Ma.

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Communicated by Marcos Eduardo Valle.

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This work is supported by National Natural Science Foundation of China (No. 61273004) and the Natural Science Foundation of Hebei province (No. F2021203061).

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Mao, D., Ma, Y. Robust \({{H}_{\infty }}\) control for uncertain Takagi–Sugeno fuzzy systems with state and input time-varying delays. Comp. Appl. Math. 41, 195 (2022). https://doi.org/10.1007/s40314-022-01879-2

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