Design of 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 controller for discrete-time-varying delay systems with missing measurements

This work addresses 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 for a class of discrete-time-varying delay systems with missing measurements, when the uncertain parameters are inside a given convex polytope. The first step in applying a model transformation is to use a three-term approximation for delayed state variables, which leads to lower approximation error than other methods. By utilizing scaled small-gain theorem and Lyapunov–Krasovskii functional methods, sufficient conditions for the robust stability of the filtering error system with a prescribed 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} performance level are obtained. The use of the scaled small-gain theorem for the robust stability of discrete-time-varying systems with missing measurements has not been studied before in the literature. This represents the main novelty of this paper. Some previous results based on LMIs are found to be particular cases of that obtained in this paper. Finally, numerical examples are given to illustrate the efficiency of the proposed methodology.