Title: H_∞ model reduction of discrete-time 2D T-S fuzzy systems in finite frequency ranges

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

Addresses: Faculty of Sciences, University Sidi Mohamed Ben Abdellah, Dhar El Mehraz, Fez, Morocco; LISAC Lab, 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 ' Faculty of Sciences, University Sidi Mohamed Ben Abdellah, Dhar El Mehraz, Fez, Morocco; LISAC Lab, Department of Physics, B.P. 1796 Fes-Atlas, Morocco ' Faculty of Sciences, University Sidi Mohamed Ben Abdellah, Dhar El Mehraz, Fez, Morocco; LISAC Lab, 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.

DOI: 10.1504/IJMIC.2021.119032

International Journal of Modelling, Identification and Control, 2021 Vol.37 No.1, pp.22 - 31

Received: 20 Apr 2020
Accepted: 24 Nov 2020
Published online: 18 Nov 2021 *

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