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This paper investigates the robust exponential stability for discrete-time Cohen-Grossberg neural networks with both time-varying and distributed delays. By constructing a novel Lyapunov-Krasovskii functional and introducing some free-weighting matrices, two delay-dependent sufficient conditions are obtained by using convex combination. These criteria are presented in terms of LMIs and their feasibility can be easily checked with the help of LMI in Matlab Toolbox. In addition, the activation function can be described more generally, which generalizes those earlier methods. Finally, the effectiveness of the obtained results is further illustrated by a numerical example in comparison with the existent ones.