A finite frequency approach for H-infinity model reduction of T-S fuzzy discrete-time systems

A. El-Amrani (1, 2) , B. Boukili (1) , A. Hmamed (3) , A. El Hajjaji (4) , I Boumhidi

1 USMBA - Université Sidi Mohamed Ben Abdellah
2 UPJV - Université de Picardie Jules Verne
3 LESSI-départment de physique
4 MIS - Modélisation, Information et Systèmes - UR UPJV 4290

This paper deals with H-infinity model reduction problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with external disturbances assumed belong to finite frequency (FF) ranges. By applying the generalized Kalman-Yakubovich-Popov (gKYP) lemma, Projection lemma and introducing some key matrices to eliminate the product terms between the reduced-order parameters and the Lypunov matrices, an improved conditions is obtained for analyzing the H-infinity performance of the error system. Then sufficient condition in terms of linear matrix Inequalities (LMIs) are established for designing reduced-order model with a guaranteed H-infinity performance level. Finally, we demonstrate via numerical example that our method can achieve much smaller approximation error than existing results.

Domaines: Automatique / Robotique

A. El-Amrani, B. Boukili, A. Hmamed, A. El Hajjaji, I Boumhidi. A finite frequency approach for H-infinity model reduction of T-S fuzzy discrete-time systems. 2019 8TH INTERNATIONAL CONFERENCE ON SYSTEMS AND CONTROL (ICSC'19), Oct 2019, Marrakech, Morocco. pp.471-475. ⟨hal-03633203⟩