Title: Robust over finite frequency ranges H model reduction for uncertain 2D continuous systems

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

Addresses: Faculty of Sciences Dhar El Mehraz, LESSI, 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, LESSI, Department of Physics, B.P. 1796 Fes-Atlas, Morocco ' Faculty of Sciences Dhar El Mehraz, LESSI, Department of Physics, B.P. 1796 Fes-Atlas, Morocco ' Faculty of Sciences Dhar El Mehraz, LESSI, Department of Physics, B.P. 1796 Fes-Atlas, Morocco

Abstract: This paper deals with the problem of robust H model reduction for two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties, 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 continuous systems 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, homogeneous polynomially parameter-dependent matrices, Finsler's lemma and we introduce many slack matrices, sufficient conditions for the existence of H model reduction for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). To highlight the effectiveness of the proposed H model reduction design, two illustrative examples are given.

Keywords: multidimensional systems; uncertain systems; model reduction; finite frequency; Roesser models; linear matrix inequality; H performance.

DOI: 10.1504/IJSSE.2020.109140

International Journal of System of Systems Engineering, 2020 Vol.10 No.2, pp.108 - 127

Received: 04 Jul 2019
Accepted: 22 Nov 2019

Published online: 18 Aug 2020 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article