• discrete-time singular systems;
  • time-varying interval delay;
  • H ∞  control;
  • bounded real lemma;
  • cone complementarity linearization (CCL)


This paper investigates the state feedback robust H ∞  control problem of a class of discrete-time singular systems with norm-bounded uncertainties and interval time-varying delays in state and input. A new bounded real lemma for discrete-time singular systems with a pair of time-varying interval state delays is first investigated. Mathematical comparisons of the new bounded real lemma and two existing ones are presented. Then, on the basis of the bounded real lemma proposed here, a sufficient condition in the form of nonlinear matrix inequality, such that the considered state feedback robust H ∞  control problem is solvable, is given. In order to solve the nonlinear matrix inequality, a cone complementarity linearization algorithm is offered. Several numerical examples are presented to show the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.