Stability analysis of uncertain discrete-time systems with time-varying delays using Difference-Algebraic Representation

This paper addresses the stability analysis of uncertain discrete-time delayed systems described by Difference-Algebraic Representations (DAR). This kind of representation allows dealing with rational functions of the state as well as uncertain parameters. New delay-dependent Linear Matrix Inequalities based-conditions are obtained with a parameter-dependent Lyapunov-Krasovskii functional jointly with the Wirtinger-based summation inequality and the delay-dependent Moon's inequality with a suitable augmented vector. Numerical examples illustrate the potential and effectiveness of the proposed conditions.