Title: H_∞ model reduction design in finite frequency ranges for discrete-time Takagi-Sugeno fuzzy systems

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

Addresses: LISAC Laboratory, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco ' LISAC Laboratory, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco ' MIS Lab, University of Picardie, Jules-Vernes, UFR of Sciences, 33 rue, St Leu, 80000, Amiens, France ' LISAC Laboratory, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco ' LISAC Laboratory, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco

Abstract: This paper addresses the problem of H_∞ model reduction design in finite frequency ranges for discrete-time nonlinear systems. With the aid of the generalised Kalman-Yakubovich-Popov (gKYP) lemma, the Lyapunov theory, and some matrix inequality techniques, sufficient conditions for the finite frequency model reduction problem are derived. The design conditions are given in terms of sufficient parameter-dependent linear matrix inequalities that can be solved through relaxations based on semi-definite programming. The advantages of the proposed approach are illustrated through numerical examples and comparisons with other available techniques.

Keywords: model reduction; finite frequency; linear matrix inequalities; Takagi-Sugeno (T-S) model; H_∞ performance; Lyapunov approach; discrete-time nonlinear systems.

DOI: 10.1504/IJSSE.2021.116047

International Journal of System of Systems Engineering, 2021 Vol.11 No.2, pp.89 - 104

Received: 26 Jun 2020
Accepted: 08 Sep 2020
Published online: 06 Jul 2021 *

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