The aim of my presentation is to present new conditions for stability for the class of system governed by linear difference equations with distributed delay, by using the Lyapunov-Krasovskii approach. This approach consists to involve stability conditions of the form of a convex optimization problem. So, I propose sufficient conditions providing the decay estimate of the response of linear difference equations with distributed delay. These conditions are less conservative than previous results in the literature. This stability analysis is extended also to the case of systems with time-varying delays.