H∞ control for discrete-time uncertain singular systems with interval time-varying state and input delays

This study focuses on the H_∞ control problem of a class of discrete-time uncertain singular systems with interval time-varying state and input delays. A sufficient condition, in the form of linear matrix inequality (LMI) with nonlinear constraints, for the existence of H_∞ state feedback controller is given by combining Lyapunov approach and LMI technique. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. As a medium step, a new bounded real lemma for discrete-time singular systems with a pair of interval time-varying state delays is obtained. Two numerical examples are provided to show the applicability of the proposed approach.