Stochastic state estimation for neural networks with distributed delays and Markovian jump

This paper investigates the problem of state estimation for Markovian jump Hopfield neural networks (MJHNNs) with discrete and distributed delays. The MJHNN model, whose neuron activation function and nonlinear perturbation of the measurement equation satisfy sector-bounded conditions, is first considered and it is more general than those models studied in the literature. An estimator that guarantees the mean-square exponential stability of the corresponding error state system is designed. Moreover, a mean-square exponential stability condition for MJHNNs with delays is presented. The results are dependent upon both discrete and distributed delays. More importantly, all of the model transformations, cross-terms bounding techniques and free additional matrix variables are avoided in the derivation, so the results obtained have less conservatism and simpler formulations than the existing ones. Numerical examples are given which demonstrate the validity of the theoretical results.