An LMI approach to worst case analysis for fault detection observers

This paper systematically formulates the worst-case fault sensitivity analysis problem for fault detection observers. The lowest level of a fault detector´s fault sensitivity is defined as an H_ index. A full characterization of the H_ index is given in terms of matrix equalities and inequalities as a dual of the bounded real lemma. Necessary and sufficient conditions are given to find a lower bound of H_ index, which can be calculated efficiently by linear matrix inequality (LMI) solvers. In addition, the analysis problem with respect to a finite frequency band is also solved by adding weighting filters, which is very useful for strictly proper systems. The necessary and sufficient conditions for input observability are also given, which is necessary condition for a fault detection observer to have a nonzero worst-case fault sensitivity. The effectiveness of the proposed approaches is shown by numerical exampled.