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This article focuses on the impulsive synchronization of chaotic neural networks (CNNs) with time-varying delays subject to actuator saturation. By constructing discontinuous Lyapunov function and employing linear matrix inequality (LMI) approach, some sufficient conditions are derived to guarantee the synchronization object of the delayed chaotic neural networks. In addition, the control methods in this article have no strict requirements on the size of time delay and the actuator saturation domain, which is more flexible and practical in real system. Finally, a numerical example is given to verify the effectiveness of the proposed method.