Fault detection and isolation for unstable linear systems

In the design of a residual generator for an unstable plant, the unstable modes are made unobservable from the residual vector. We point out that this cannot be achieved in practice due to the discrepancy between 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-product, we provide expressions which can be used to quantify the effect of modeling uncertainties on the performance of a residual generator. The factorization approach to control theory is used for the developments