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Control of Time Delay Polynomial Fuzzy Model Subject to Actuator Saturation

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Abstract

This article is concerned with the design of polynomial fuzzy controller for a class of polynomial fuzzy model subject to both state delay and actuator saturation. Based on polytopic model of the input saturation, two design methods are proposed. In the first method, a specific Lyapunov Krasovskii function is proposed to transform the nonconvex sum of squares (SOS) conditions into convex SOS ones. The second method overcomes the restriction of the first method by bounding the state derivative. The obtained results are formulated in terms of SOS matrices which can be symbolically and numerically solved via the SOSTOOLS and the SeDuMi. Moreover, an attractive region of initial states that ensures asymptotic stability of polynomial fuzzy model is determined. Two numerical examples are given to show the effectiveness of the proposed methods.

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Authors and Affiliations

  1. National School of Engineering, University of Sfax, Sfax, Tunisia

    Hamdi Gassara & Mohamed Chaabane

  2. Modeling, Information, Systems Laboratory (MIS Lab.), University of Picardie Jules Verne, Amiens, France

    Ahmed El Hajjaji

Authors
  1. Hamdi Gassara
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  2. Ahmed El Hajjaji
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  3. Mohamed Chaabane
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Correspondence to Ahmed El Hajjaji.

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Gassara, H., El Hajjaji, A. & Chaabane, M. Control of Time Delay Polynomial Fuzzy Model Subject to Actuator Saturation. Int. J. Fuzzy Syst. 18, 763–772 (2016). https://doi.org/10.1007/s40815-015-0133-1

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  • DOI: https://doi.org/10.1007/s40815-015-0133-1

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