State estimation for Markovian jump Hopfield neural networks with mixed time delays - Guo, Lili; Huang, Wanhui (Frontiers in Physics, 2024)
This paper deals with the issue of state estimation concerning a category of Markovian jump Hopfield neural networks (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 meansquare 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.