Delay-dependent H∞ Control for Systems with Two Additive Time-vary Delays

This paper is concerned with the delay-dependent H∞ control problem for systems with two additive time-varying delays. We construct a new Lyapunov functional and give a tighter upper bound for the derivative of the Lyapunov functional, then employ a new method, the polyhedron method, to test the negative definiteness of the upper bound. New delaydependent stability criteria are thus derived, which are less conservative than some existing ones. Based on the stability criteria a state feedback controller is constructed to guarantee that the closed-loop system is asymptotically stable with a prescribed H∞ disturbance attenuation level. Finally examples are given to show the advantages of the stability criteria and the effectiveness of the proposed control method.