This chapter is concerned with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}_\infty $$\end{document} fault estimation of a class of parabolic systems with distributed inputs and outputs. The fault in the considered parabolic system is characterized by a minimal state-space description of a low-pass filter, which incorporates fault’s prior knowledge. The fault estimator is designed by using the Lyapunov theory and linear matrix inequalities (LMIs) approach. The sufficient conditions in the form of LMIs are developed to ensure the resulting error system is asymptotically stable with an optimized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}_\infty $$\end{document} disturbance attenuation level. The designed estimator gain matrices can be easily determined by using the standard optimization toolboxes. Finally, two numerical examples and simulation results are provided to illustrate the effectiveness and advantages of the obtained results.


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