Synchronization of cellular neural networks with time-varying delay is discussed in this letter. Based on Razumikhin theorem, a guaranteed cost synchronous controller is given. Unlike Lyapunov-Krasovskii analysis process, there is no constraint on the change rate of time delay. The saturated terms emerging in the Razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by Lipschitz condition and vector inequality, which will bring more conservatism. Then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form, with the help of a sufficient and necessary transformation condition. The minimization of the guaranteed cost is studied, and a further criterion for getting the controller is presented. Finally, the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time-varying delay cellular neural networks.

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