Delay-dependent robust $H_\infty$ control for singular systems with multiple delays

This paper deals with the problem of delay dependent robust $H_\infty$ control for singular systems with multiple delays. Based on Lyapunov--Krasovskii functional approach, an improved delay-dependent bounded real lemma (BRL) for singular time-delay systems is established without using any model transformations and bounding techniques on the cross product terms. Then by applying the obtained BRL, a delay dependent condition for the existence of a robust state feedback controller, which guarantees the closed loop system to be regular, impulse free, robustly stable and satisfies a prescribed $H_\infty$ performance index, is proposed in terms of a nonlinear matrix inequality. The explicit expression for the $H_\infty$ controller is designed by using linear matrix inequalities and the cone complementarity iterative linearzation algorithm. Numerical examples are proposed to illustrate the effectiveness of the proposed method. doi:10.1017/S144618110900012