Title: Finite frequency H_∞ filter design for T-S fuzzy continuous systems

Authors: Abderrahim El-Amrani; Ahmed El Hajjaji; Bensalem Boukili; Ismail Boumhidi; Abdelaziz Hmamed

Addresses: LISAC Lab, Faculty of Sciences Dhar El Mehraz, Department of Physics, B.P. 1796 Fes-Atlas, Morocco ' MIS Lab, University of Picardie, Jules-Vernes, UFR of Sciences, 33 rue, St Leu, 80000 Amiens, France ' LISAC Lab, Faculty of Sciences Dhar El Mehraz, Department of Physics, B.P. 1796 Fes-Atlas, Morocco ' LISAC Lab, Faculty of Sciences Dhar El Mehraz, Department of Physics, B.P. 1796 Fes-Atlas, Morocco ' LISAC Lab, Faculty of Sciences Dhar El Mehraz, Department of Physics, B.P. 1796 Fes-Atlas, Morocco

Abstract: This paper addresses the problem of finite frequency (FF) H_∞ filter design for nonlinear continuous-time systems described by Takagi-Sugeno (T-S) fuzzy models. The objective is to provide a new design sufficient condition via linear matrix inequality (LMI) formulation, ensuring both the stability of the filtering error system and H_∞ performance when frequency ranges of noises are known beforehand. Less conservative results are obtained by using the generalised Kalman-Yakubovich-Popov (gKYP) lemma, Finsler's lemma and some independent matrices. Finally, three examples are given to show that the developed FF distributed filter design method has less conservation than the method for the entire frequency region.

Keywords: finite frequency; nonlinear systems; H_∞ performance; filter design; Takagi-Sugeno (T-S) model; ; linear matrix inequality; H_∞ performance.

DOI: 10.1504/IJSSE.2020.112309

International Journal of System of Systems Engineering, 2020 Vol.10 No.4, pp.367 - 396

Received: 18 Feb 2020
Accepted: 24 Jun 2020
Published online: 07 Jan 2021 *

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