In this paper, the design of filters for fault detection and diagnosis using a post filter and an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimization approach is investigated. The problem is translated into an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output feedback control and some classical methods can be used to solve it. The design of the detection filter is done in two steps, and the filter allows the detection and the isolation of multiple faults, in presence of perturbation and uncertainties.