Title: Improved finite frequency H_∞ filtering for Takagi-Sugeno fuzzy systems

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

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

Abstract: This paper investigates the design problem of H_∞ filtering for discrete nonlinear systems in the Takagi-Sugeno (T-S) form. Our aim is to design a new filter guaranteeing an H_∞ performance level in specific finite frequency (FF) ranges. Using the well-known generalised Kalman Yakubovich Popov lemma, Finsler's lemma, sufficient conditions for the existence of H_∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). Two examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.

Keywords: finite frequency; H_∞ filtering; Takagi-Sugeno; fuzzy systems.

DOI: 10.1504/IJSCC.2020.105391

International Journal of Systems, Control and Communications, 2020 Vol.11 No.1, pp.1 - 24

Received: 12 Feb 2018
Accepted: 19 Jan 2019
Published online: 27 Feb 2020 *

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