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In this article, a controller with delay impulse is applied to a neural network (NN) with time-varying delays. Firstly, the lag synchronization of the system is discussed. In addition, a sufficient condition for guaranteed lag synchronization requiring all state information is derived by using linear matrix inequality (LMI). In particular, the main results of neural networks (NNs) with time-varying delays and partial unmeasured states are studied by using the delay impulsive control gain matrix derived from dimension expansion. Finally, we will give two examples, both of which can confirm the validity of the results.