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New Polynomial Lyapunov Functional Approach to Observer-Based Control for Polynomial Fuzzy Systems with Time Delay

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Abstract

This paper presents a new Line-integral polynomial Lyapunov functional approach for observer-based control for a class of polynomial fuzzy systems with time delay and unmeasured state variables. To guarantee the global asymptotic stability and estimation error convergence, a design method is proposed. In this work we consider a Line-integral polynomial Lyapunov function in which the Lyapunov matrices are polynomial matrices depending not only of the estimated states but also of the estimated delayed states and we use the dual system to reduce the computational efforts. The design conditions are established in terms of Sum Of Squares (SOS) which can be numerically and symbolically solved via the recent developed SOSTOOLS and a Semi-Definite Program solver. Finally, numerical examples are proposed to show the validity and applicability of the proposed results .

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Authors and Affiliations

  1. STA Lab, National School of Engineers, University of Sfax, Sfax, Tunisia

    Imen Iben Ammar, Hamdi Gassara & Mohamed Chaabane

  2. Modeling, Information and Systems Laboratory (MIS Lab.), University of Picardie Jules Verne, 80000, Amiens, France

    Ahmed El Hajjaji

Authors
  1. Imen Iben Ammar
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  2. Hamdi Gassara
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  3. Ahmed El Hajjaji
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  4. Mohamed Chaabane
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Correspondence to Ahmed El Hajjaji.

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Ammar, I.I., Gassara, H., El Hajjaji, A. et al. New Polynomial Lyapunov Functional Approach to Observer-Based Control for Polynomial Fuzzy Systems with Time Delay. Int. J. Fuzzy Syst. 20, 1057–1068 (2018). https://doi.org/10.1007/s40815-017-0425-8

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  • DOI: https://doi.org/10.1007/s40815-017-0425-8

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