H∞ Model Reduction of Continuous-Time Periodic Piecewise Systems over a FiniteFrequency Range

Abstract

International audienceThis paper presents a novel and effective methodology for designing reduced-order models of continuoustime linear periodic piecewise systems, with a finite-frequency (FF) range of the disturbance input. Theproposed approach is based on Linear Matrix Inequalities (LMIs) and ensures that a stability conditionand a finite-frequency H∞ performance analysis condition are developed. The key contribution lies in thedevelopment of an extended version of the generalized Kalman-Yakubovich-Popov (gKYP) lemma, specifically adapted to the class of periodic piecewise systems. By exploiting the structural properties of thesesystems and applying the projection lemma, new sufficient LMI-based conditions are derived to ensure theasymptotic stability of the estimation error dynamics, while achieving robust H∞ performance within thetargeted frequency band of the exogenous disturbance. Two numerical examples are presented to validatethe proposed method, demonstrating its feasibility and improved accuracy in terms of reduction error