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New Approach to H∞ Filtering for Fuzzy Systems in Finite Frequency Domain

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Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 427))

Abstract

This paper is concerned with the problem of finite frequency (FF) H∞ full-order filtering design for discrete-time nonlinear systems, in the Takagi-Sugeno form. We choose basis dependent Lyapunov function and using the finite frequency l 2 gain definition, and the generalized S-procedure lemma, we propose sufficient conditions, ensuring that the filtering error system is stable and has a minimized H∞ attenuation level in the low-, middle-, and high-frequency domains. In order to linearize and relax the obtained conditions, we apply the Finsler’s lemma twice, and we obtain a set of new sufficient conditions for the existence of the H∞ filter in terms of linear matrix inequalities (LMIs). Then, we show how we can calculate the filter gain matrices by using these conditions. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.

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Author information

Authors and Affiliations

  1. Modeling, Information, System (MIS) Laboratory, University of Picardie Jules Verne, UFR Sciences, Street Saint Leu, 80000, Amiens, France

    D. El Hellani & A. El Hajjaji

  2. ESIGETEL, EFREI Group, 30-32 Avenue of the Republic, 94800, Villejuif, France

    D. El Hellani & R. Ceschi

Authors
  1. D. El Hellani
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  2. A. El Hajjaji
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  3. R. Ceschi
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Corresponding author

Correspondence to D. El Hellani .

Editor information

Editors and Affiliations

  1. Sci. Network for Innovation & Rec. Exell, Machine Intelligence Research Labs (MIR, Auburn, Washington, USA

    Ajith Abraham

  2. Membre du Groupe Efrei, ESIGETEL, Villejuif, France

    Katarzyna Wegrzyn-Wolska

  3. Faculty of Computers & Information, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

  4. VSB-Technical University of Ostrava, Ostrava, Czech Republic

    Vaclav Snasel

  5. ENIS, University of Sfax, Sfax, Tunisia

    Adel M. Alimi

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El Hellani, D., El Hajjaji, A., Ceschi, R. (2016). New Approach to H∞ Filtering for Fuzzy Systems in Finite Frequency Domain. In: Abraham, A., Wegrzyn-Wolska, K., Hassanien, A., Snasel, V., Alimi, A. (eds) Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015. Advances in Intelligent Systems and Computing, vol 427. Springer, Cham. https://doi.org/10.1007/978-3-319-29504-6_50

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  • DOI: https://doi.org/10.1007/978-3-319-29504-6_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29503-9

  • Online ISBN: 978-3-319-29504-6

  • eBook Packages: EngineeringEngineering (R0)

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