Robust H∞ control for discrete singular systems with time-varying delays and uncertainties

This paper concentrates on the H∞ control problem of discrete singular systems with time-varying delay and norm-bounded uncertainties. Firstly, a novel bounded real lemma is established for discrete-time singular systems with time-varying delay. Then, with Lyapunov function, an improved reciprocally convex combination approach and linear matrix inequality (LMI) technique, a sufficient criterion for the existence of the H∞ state feedback controller is given in the form of matrix inequalities with nonlinear constraints. The cone complementarity linearization (CCL) algorithm is adopted to solve the nonlinear constraints. Finally, a numerical example is presented to illustrate the advantage of the proposed approach.