Non-fragile robust H∞ control for uncertain discrete-time singular systems with time-varying delays

Abstract

In this paper, the problem of delay-dependent non-fragile robust H∞ control for a class of discrete-time singular systems with state-delay and parameter uncertainties is investigated. Based on singular value decomposition approach, a delay-dependent sufficient condition for the H∞ control problem for a class of discrete-time singular systems is proposed by constructing generalized Lyapunov–Krasovskii function and a new difference inequality. A memoryless state feedback controller under controller gain perturbations is designed, which guarantees that, for all admissible uncertainties, the resultant closed-loop system is regular, causal, and stable with an H∞ norm bound constraint. Numerical examples in the last will show that our results have the better performance in conservativeness than some results reported in the literature.