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

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.
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https://hal.inria.fr/hal-03024974
Contributor : Ahmed El Hajjaji <>
Submitted on : Thursday, November 26, 2020 - 10:03:01 AM
Last modification on : Friday, November 27, 2020 - 3:04:59 AM

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Abderrahim El Amrani, Ahmed El Hajjaji, Bensalem Boukili, Ismail Boumhidi, Abdelaziz Hmamed. Robust over finite frequency ranges H∞ model reduction for uncertain 2D continuous systems. International Journal of System of Systems Engineering, 2020, 10 (2), pp.108. ⟨10.1504/IJSSE.2020.109140⟩. ⟨hal-03024974⟩

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