Robust dissipativity and passivity based state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays

In this paper, the problem of robust state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays is investigated based on dissipativity and passivity theory. The parameters of the neural networks are subject to the switching from one mode to another according to a Markov chain. By using the Lyapunov–Krasovskii functional together with linear matrix inequality approach, a new set of sufficient conditions are derived for the existence of state estimator such that the error state system is strictly (Q,S,R)-γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma $$\end{document}-dissipative. Finally, numerical examples are addressed to show the effectiveness of the proposed design method .