In the design of a residual generator for an unstable plant, the unsta
ble modes are made unobservable from the residual vector. We point out
that this cannot be achieved in practice due to the discrepancy betwe
en the estimated model and the ''true'' plant model. Hence, we deduce
that it is not possible to design a residual generator for an unstable
plant, unless it is stabilized by an adequate controller. As a by-pro
duct, we provide expressions which can be used to quantity the effect
of modeling uncertainties on the performance of a residual generator.
The factorization approach to control theory is used for the developme
nts.