Delay-dependent robust H∞ control for uncertain discrete singular linear time-delay systems

The problem of delay-dependent robust H_∞ control for a class of uncertain discrete singular linear time-delay systems is investigated. With the introduction of a null matrix of singular matrix E and a free matrix to draw the relation between slow states and fast states, a delay-dependent bounded real lemma is obtained for the considered discrete singular linear time-delay system to be regular, causal, stable and satisfy some prescribed H_∞ performance. Based on this, the problem of robust H_∞ control is solved and an explicit expression of the desired state feedback control law is given. The obtained results are expressed in terms of linear matrix inequalities that are easily solved numerically. Numerical examples are given to demonstrate the effectiveness of the proposed methods.