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

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

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

Abstract: This paper considers the problem of H_∞ model reduction design for two-dimensional (2D) discrete-time Takagi-Sugeno (T-S) fuzzy systems described by Roesser model, over finite frequency (FF) domain. The problem to be solved in the paper is to find a reduced-order model such that the approximation error system is asymptotically stable, which is able to approximate the original T-S fuzzy system with comparatively small and minimised H_∞ performance when frequency ranges of noises are known beforehand. Via the use of the generalised Kalman Yakubovich Popov (gKYP) lemma, new design conditions guaranteeing the FF H_∞ model reduction are established in terms of linear matrix inequalities (LMIs). To highlight the effectiveness of the proposed H_∞ model reduction design, a numerical example is given to illustrate the effectiveness and the less conservativeness of the proposed approach.

Keywords: model reduction; multidimensional systems; Roesser models; finite frequency; H_∞ performance.

DOI: 10.1504/IJAACS.2023.132514

International Journal of Autonomous and Adaptive Communications Systems, 2023 Vol.16 No.4, pp.404 - 418

Received: 24 May 2020
Accepted: 23 Dec 2020
Published online: 25 Jul 2023 *

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