Robust finite-frequency H-infinity model reduction for uncertain 2D discrete systems

Abderrahim El-Amrani (1, 2) , Ahmed El Hajjaji (2) , Jerome Bosche (2) , Abdel Aitouche (3, 4)

1 LESSI-départment de physique
2 MIS - Modélisation, Information et Systèmes - UR UPJV 4290
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
4 JUNIA - JUNIA

In this work, robustness and convergence properties of model reduction are investigated for discrete two-dimensional (2D) systems in the Fornasini-Marchesini (F-M) model with polytopic uncertainties. The goal is to design a reduced order model minimizing H-infinity performance in a known finite-frequency (FF) area of the noises able to reproduce the behavior of the uncertain 2D original system. Using Lyapunov function and generalized Kalman Yakubovich Popov (gKYP) lemma, sufficient conditions for the existence of the FF reduced order design approach are formulated as feasibility of a set of Linear Matrix Inequalities (LMIs). Numerical simulations are given to illustrate the validity and feasibility of the designed reduced-order model.

Domaines: Automatique

Abderrahim El-Amrani, Ahmed El Hajjaji, Jerome Bosche, Abdel Aitouche. Robust finite-frequency H-infinity model reduction for uncertain 2D discrete systems. 2022 30th Mediterranean Conference on Control and Automation (MED), Jun 2022, Athènes, Greece. pp.158-163, ⟨10.1109/MED54222.2022.9837190⟩. ⟨hal-03833277⟩