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In this paper, we consider discrete delay systems and obtain conditions for global uniform exponential stability. Our approach is based on the use of the Razumikhin technique and the Lyapunov function method. In the second part of the paper, we use our stability results to derive exponential synchronization criteria for discrete dynamical networks with coupling time delays. We explicitly consider the case of networks with complex structures, such as networks with chaotic nodes, which have great practical importance in the area of secure communications.