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Reliable \(H_{\infty }\) Stabilization of Fuzzy Systems with Random Delay Via Nonlinear Retarded Control

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Abstract

In this paper, the robust reliable \(H_\infty \) control problem has been investigated for a class of nonlinear discrete-time TS fuzzy systems with random delay. In particular, the proposed fuzzy system consists of local nonlinear models with set of fuzzy rules, but the conventional TS fuzzy systems has local linear models. Our attention is focused on the design of a feedback reliable nonlinear retarded control law to ensure the robust asymptotic stability for nonlinear discrete-time TS fuzzy system with admissible uncertainties as well as actuator failure cases and random delay. In particular, by using an input delay approach, the random delay with stochastic parameters in the system matrices is introduced in the system model. Based on the Lyapunov approach, firstly, a sufficient condition for asymptotic stability is proposed for TS fuzzy systems in the presence of actuator failures. Then, a robust reliable \(H_\infty \) control is designed for the uncertain TS fuzzy system by solving a strict linear matrix inequalities using the available numerical software. Finally, a numerical example based on real-time ball and beam system is provided to validate the effectiveness of the proposed design technique.

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant founded by the BrainKorea21plus (No. 21A20131400002).

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440 746, Republic of Korea

    R. Sakthivel

  2. Department of Mathematics, Al-Ameen Engineering College, Erode, 638 104, India

    K. Sundareswari

  3. Department of Mathematics, Anna University-Regional centre, Coimbatore, 641 047, India

    K. Mathiyalagan & Srimanta Santra

Authors
  1. R. Sakthivel
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  2. K. Sundareswari
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  3. K. Mathiyalagan
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  4. Srimanta Santra
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Correspondence to K. Mathiyalagan.

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Sakthivel, R., Sundareswari, K., Mathiyalagan, K. et al. Reliable \(H_{\infty }\) Stabilization of Fuzzy Systems with Random Delay Via Nonlinear Retarded Control. Circuits Syst Signal Process 35, 1123–1145 (2016). https://doi.org/10.1007/s00034-015-0115-4

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  • DOI: https://doi.org/10.1007/s00034-015-0115-4

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