LAUSR

This paper investigates the asymptotic state estimation problem for linear systems with sensor and actuator faults, where the faults are modeled via multiple modes. For the case of sensor faults, we first introduce a new notion of detectability, i.e., detectability of system against sensor faults. The notion helps to address the question of whether it is possible to asymptotically estimate the system state by using the control input and system output, irrespective of which mode the system is in and what values the fault signals are. A necessary and sufficient condition for the system to be detectable against sensor faults is given, and then two switched observers are proposed for asymptotic state estimation with the help of maximin strategy. For the system with ℓ fault modes, we provide the explicit form of the switched observer, which is based on a bank of ℓ(ℓ+1)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\ell(\ell+1)}{2}$$\end{document} Luenberger-like or sliding-mode observers. Furthermore, extensions to the case of sensor and actuator faults are further studied. Finally, a simulation example of a reduced-order aircraft system is provided to show the effectiveness of the proposed approaches.