H∞ Filtering for General Delayed Nonlinear Stochastic Systems with Markov Jumps

This paper is concerned with the robust H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} filtering problem of nonlinear stochastic delayed systems with Markov jumps, where time delay exists in state equation, measurement equation and controlled output. Firstly, by introducing a nonlinear stochastic bounded real lemma, we present the H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} filter design via solving a set of Hamilton-Jacobi inequalities (HJIs). Secondly, by using fuzzy approach, the H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} filter can be designed via solving a set of Linear Matrix inequalities instead of HJIs. Finally, two numerical examples are given to show the effectiveness of our results.