Robust Mixed H2/H∞ Control of Uncertain Neutral Systems with Time-Varying Delays

This paper considers the problem of robust mixed H 2/H ∞ delayed state feedback control for a class of uncertain neutral systems with time-varying discrete and distributed delays. Based on the Lyapunov-Krasovskii functional theory, new required sufficient conditions are established in terms of delay-range-dependent linear matrix inequalities (LMIs) for the stability and stabilization of the considered system using some free matrices. The desired robust mixed H 2/H ∞ delayed control is derived based on a convex optimization method such that the resulting closed-loop system is asymptotically stable and satisfies H 2 performance with a guaranteed cost and a prescribed level of H ∞ performance, simultaneously. Finally, a numerical example is given to illustrate the effectiveness of our approach.