Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated. By constructing a novel switched Lyapunov–Krasovskii functional, a delay-dependent criterion for the unforced system to be regular, causal and uniformly asymptotically stable is established in terms of linear matrix inequalities (LMIs). An explicit expression for the desired memoryless state feedback stabilization controller is also given. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, which are achieved by considering additionally useful terms (ignored in previous methods) when estimating the upper bound of the forward difference of the Lyapunov–Krasovskii functional and by avoiding utilizing any model augmentation transformation. Some numerical examples are provided to illustrate the validity of the proposed methods.