State estimation for discrete-time recurrent neural networks with time-varying delay is investigated. A state
estimator to estimate the neuron states is designed through available output measurements. Under a weaker assumption on
the activation functions, by constructing a new Lyapunov functional, introducing a free weighting matrix and employing the
Jensen inequality, a sufficient condition is established to ensure the globally exponential stability of the error system. The
condition is dependent on both the lower bound and upper bound of the time-varying delay, and is given in terms of linear
matrix inequality. Finally, a numerical example shows the effectiveness of the proposed method.