This paper investigates the stabilization problem of neural networks with unbounded continuously distributed delays via impulsive control. By establishing an impulsive infinite delay differential inequality from the impulsive control point of view, some sufficient conditions ensuring the existence and global exponential stabilization of the unique equilibrium point are derived. Our result shows that impulses can be used to globally and exponentially stabilize the neural networks with unbounded continuously distributed delays if they are not originally stable or exponentially stable. Finally, two examples with their simulations are given to show the effectiveness of the proposed method.

In this paper, the exponential state estimation problem for impulsive neural networks with both leakage delay and time-varying delays is investigated. Several sufficient conditions which are given in terms of linear matrix inequalities (LMIs) are derived to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable by constructing suitable Lyapunov–Krasovskii functionals and employing available output measurements and LMI technique. The obtained results are dependent on the leakage delay and upper bound of time-varying delays and independent of the derivative of time-varying delays. Moreover, some comparisons are made to contrast to some of existing results about state estimation of neural networks. Finally, two numerical examples and their computer simulations are given to show the effectiveness of proposed estimator.