Fault Detection for Switching Discrete-Time Systems with External Disturbance

This study addresses the robust fault detection problem for discrete-time switching systems under an arbitrary switching signal. Sufficient conditions building an observer are obtained by using multiple Lyapunov function and 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} methods. A sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method.