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\(H_{\infty }\) State Control for 2D Fuzzy FM Systems with Stochastic Perturbation

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Abstract

This paper investigates the \(H_{\infty }\) control problem for two-dimensional (2D) Takagi–Sugeno (T–S) fuzzy systems in a Fornasini–Marchesini second (FM II) model with stochastic perturbation. Our aim is to develop the state feedback control for 2D (T–S) fuzzy systems with stochastic perturbation and reduce the conservatism by using some slack matrices. Attention is focused on the design of the state feedback control, which guarantees the closed-loop system to be mean-square asymptotically stable and to have a prescribed \(H_{\infty }\) performance. Sufficient conditions are derived for the existence of such controls in terms of linear matrix inequalities, and the corresponding control synthesis problem, then, is solved. Numerical examples are given to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Faculty of Science Dhar El Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796, Fez, Morocco

    Bensalem Boukili & Abdelaziz Hmamed

  2. LAEPT URAC 28, Faculty of Science Semlalia, University Cadi Ayyad, BP 2390, Marrakech, Morocco

    Abdellah Benzaouia

  3. MIS Lab, UFR of Sciences, University of Picardie Jules-Vernes, 33 Rue St Leu, 80000, Amiens, France

    Ahmed El hajjaji

Authors
  1. Bensalem Boukili
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  2. Abdelaziz Hmamed
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  3. Abdellah Benzaouia
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  4. Ahmed El hajjaji
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Correspondence to Abdellah Benzaouia.

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Boukili, B., Hmamed, A., Benzaouia, A. et al. \(H_{\infty }\) State Control for 2D Fuzzy FM Systems with Stochastic Perturbation. Circuits Syst Signal Process 34, 779–796 (2015). https://doi.org/10.1007/s00034-014-9889-z

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