The proposed fault diagnosis scheme relies on a residual generation based on an adaptive observer covering linear time varying (LTV), linear parameter varying (LPV), and state-affine non-linear systems, all with bounded uncertainties. A residual evaluation is then performed by set-membership computations based on zonotopes (polytopes defined as the image of a hypercube by a linear application). The main advantage of the approach is its rigorous computation of the propagation of pre-specified modelling uncertainty bounds. Within the assumed uncertainty bounds, fault detection is guaranteed to be free of false alarm, while not being too much conservative, as illustrated on the model of a satellite.