New Approach to 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} State Estimation for Continuous-Time Nonhomogeneous Markov Jump Systems with Time-Varying Delay

This paper investigates 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} state estimation problem of continuous-time delayed nonhomogeneous Markov jump systems (NMJSs). To fully consider the nonhomogeneous transition rates (TRs) and state-related vectors, a parameter-dependent Lyapunov–Krasovskii functional (PDLKF) with triple integrals is constructed, in which the integrands in the PDLKF are all time-varying. In order to deal with the derivative of the time-varying integrands, a switched vertices approach is proposed to relax the bound assumptions in the existing works, which leads to more practical results. Based on these ingredients, a corresponding switched estimator approach is proposed to match an 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} estimator for NMJSs. The designed 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} estimator is related to the switched rule, which is more general than nonswitched estimators in the previous works. Some examples are illustrated to show the effectiveness of the obtained results.