부산대학교 도서관

This article establishes the explicit formulas for the equivalence between fault detection filters and observers. The method relies on solving a Sylvester equation, the Schur decomposition, and algebraic manipulations. The equivalence being demonstrated valid from a generic point of view, it is shown that $H_\infty,H_-,H_{2},\text{ and }H_{2g}$ robust residual generators and $H_\infty /\mu$ fault estimators are particular cases. A numerical example and a realistic satellite's example illustrate the equivalence.