Delay-dependent H∞ control for LPV systems with fast-varying time delays

Presented in this paper is a method for stabilization and induced L₂-gain (or H_∞ norm) control of Linear Parameter-Varying (LPV) systems with fast-varying time delays. The Lyapunov-Krasovskii functional is used to derive the delay-dependent stability analysis and control synthesis conditions. In order to formulate the synthesis conditions as Linear Matrix Inequalities (LMIs), a relaxation method using slack variables is proposed. The introduction of slack variables along with the delay-dependent bounded real lemma conditions results in reduced conservatism with the proposed method. Sufficiency conditions that guarantee the existence of a parameter-dependent state feedback control law are then provided. Finally, numerical examples are presented to validate the proposed results and compare with recent work in the literature to show the improvements achieved.