Circuits, Systems, and Signal Processing

, Volume 33, Issue 6, pp 1737–1761 | Cite as

H Filtering of Two-Dimensional T-S Fuzzy Systems

  • Bensalem Boukili
  • Abdelaziz Hmamed
  • Abdellah BenzaouiaEmail author
  • Ahmed El Hajjaji


The H filtering problem for two-dimensional Takagi–Sugeno fuzzy systems described by the Fornasini–Marchesini (FM) model is studied. Attention is focused on the design of an H fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism.


Two-dimensional 2D fuzzy systems Multidimensional systems H filtering Basis-dependent Lyapunov functions 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Bensalem Boukili
    • 1
  • Abdelaziz Hmamed
    • 1
  • Abdellah Benzaouia
    • 2
    Email author
  • Ahmed El Hajjaji
    • 3
  1. 1.Department of Physics, Faculty of Sciences Dhar El MehrazUniversity of Sidi Mohamed Ben AbdellahFes-AtlasMorocco
  2. 2.Faculty of Science SemlaliaLAEPT URAC 28, University Cadi AyyadMarrakechMorocco
  3. 3.MIS-University of Picardie Jules-VernesAmiensFrance

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