Delay-dependent robust H∞ control for uncertain discrete singular time-varying delay systems based on a finite sum inequality

The problem of delay-dependent robust H_∞ control for uncertain discrete singular time-varying delay systems is addressed in this paper. The uncertainty is assumed to be norm bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma is derived and expressed in terms of linear matrix inequality(LMI). A suitable robust H_∞ state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable with disturbance attenuation level γ for all admissible uncertainties. A numerical example is given to demonstrate the applicability of the proposed method.