Robust $$L_2-L_{\infty }$$ L 2 - L ∞ Control for Uncertain Systems with Additive Delay Components

Abstract

This paper is concerned with the problem of robust $$L_2-L_\infty $$ control for a class of uncertain systems with additive time-varying delays. Delay-dependent conditions are obtained for the analysis of robust asymptotic stability of uncertain closed-loop system with two additive time-varying delays using a novel Lyapunov–Krasovskii functional which includes information belonging to a given delay range. More precisely, a new set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for achieving the required result of the closed-loop system with a prescribed $$L_2-L_\infty $$ disturbance attenuation level. In particular, Schur complement, Wirtinger’s based inequality and convex combination technique are utilized to simplify the derivation in the main results. Further, the robust control law with guaranteed energy-to-peak $$L_2-L_\infty $$ performance is designed by solving a set of LMIs. Also, it is noticed that the advantage of the obtained criterion lies in its simplicity and less conservativeness. The proposed theoretical results have been compared through numerical simulation which reveals that the obtained criteria are considerably less conservative than some existing results.