An Improved Approach to 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 for Uncertain Discrete-Time Systems with Multiple Delays

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 for a class of discrete-time systems with polytopic uncertainties and multiple time delays. Different from the most existing techniques, the novel augmented Lyapunov–Krasovskii functionals are constructed by incorporating the relationships between multiple time delays. Based on the proposed functionals and the Wirtinger-based inequality, sufficient conditions are first established under which the filtering error system is asymptotically stable and has an 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. Then, the adjusting parameters are introduced such that the filter gains can be effectively obtained by solving certain linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness and the benefit of the proposed approach.