Memory fault detection filter design for uncertain discrete-time systems with missing measurements

This paper is concerned with the problem 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} fault detection filter (FDF) design for uncertain discrete-time systems with missing measurements. The parameter uncertainties are supposed to reside in a polytopic region. And the phenomenon of missing measurements is characterized by using a stochastic variable satisfying Bernoulli random binary distribution. The main merit of the proposed method stems from the inclusion of some number of past states and past output measurements of the uncertain system in the structure of the FDF, yielding a memory fault detection filter (MFDF). The aim of the addressed problem is to design a MFDF, which ensures that the fault detection system is robustly stochastically stable and satisfies 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. Sufficient condition for the existence of the desired MFDF is formulated in terms of linear matrix inequalities (LMIs), which can be readily solved by standard numerical software. A numerical example with simulation is given to illustrate the effectiveness and advantages of the proposed method.