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This paper investigates the controller design problem for mean-square asymptotical synchronization of discrete-time neural networks with time-varying delay. We proposed the design method of synchronization controller, which considered the nonlinearity of controller input. Based on the designed controller, a delay-dependent synchronization criterion is proposed and formulated in the form of linear matrix inequalities (LMIs) by applying the Lyapunov function method. The result is extended to the delayed discrete-time neural network with uncertainty. Two numerical examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]