Stability and L2-gain Analysis for Impulsive Delay Systems via Two-sided Looped-functional

This paper investigates the problems of stability and L[in2}-gain for impulsive systems with time-delay. Inspired by the two-sided looped-functional method, a Lyapunov-like functional is established. Distinct from the previous researches, the information of the whole intervals x(tk+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x(t_k^+)$$\end{document} to x(t) and x(t) to x(tk+1) is completely exploited by the functional. Besides, a more advanced integral inequality is used and several integrals of the state are augmented, which are helpful to reduce the conservativeness. Based on the proposed method, sufficient criteria for stability and L2-gain are obtained. Numerical examples are provided to demonstrate the effect and the advantages of the proposed method.