New globally asymptotical synchronization of chaotic systems under sampled-data controller

This paper investigates the robust synchronization problem of chaotic Lur’e systems with external disturbance using sampled-data 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} controller. The new method is based on a novel construction of piecewise differentiable Lyapunov–Krasovskii functional (LKF) in the framework of an input delay approach. Compared with existing works, the new LKF makes full use of the information on the nonlinear part of the system and introduces the novel terms, which guarantees the positive of the whole LKF. The output feedback 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} synchronization controller is presented to not only guarantee stable synchronization, but also reduce the effect of external disturbance to 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} norm constraint. The proposed controller can be obtained by solving the linear matrix inequality problem. The effectiveness of the proposed method is demonstrated by the numerical simulations of Chua’s circuit.