State estimation for Markovian jump Hopfield neural networks with mixed time delays

Markovian jump Hopfield NNs (MJHNNs) have received considerable attention due to their potential for application in various areas. This paper deals with the issue of state estimation concerning a category of MJHNNs with discrete and distributed delays. Both time-invariant and time-variant discrete delay cases are taken into account. The objective is to design full-order state estimators such that the filtering error systems exhibit exponential stability in the mean-square sense. Two sufficient conditions on the mean-square exponential stability of MJHNNs are established utilizing augmented Lyapunov–Krasovskii functionals, the Wirtinger–based integral inequality, the Bessel-Legendre inequality, and the convex combination inequality. Then, linear matrix inequalities-based design methods for the required estimators are developed through eliminating nonlinear coupling terms. The feasibility of these linear matrix inequalities can be readily verified via available Matlab software, thus enabling numerically tractable implementation of the proposed design methods. Finally, two numerical examples with simulations are provided to demonstrate the applicability and less conservatism of the proposed stability criteria and estimators. Lastly, two numerical examples are given to demonstrate the applicability and reduced conservatism of the proposed stability criteria and estimator design methods. Future research could explore further refinement of these analysis and design results, and exporing their extention to more complex neural network models.