By the Lyapunov function method, combined with the inequality techniques, some criteria are established to ensure the existence, uniqueness and global exponential stability of the periodic solution for a class of impulsive neural networks. The results obtained only require the activation functions to be globally Lipschitz continuous without assuming their boundedness, monotonicity or differentiability. The conditions are easy to check in practice and they can be applied to design globally exponentially periodic impulsive neural networks.
