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This article proposes a robust set-membership fault detection method based on the use of polytopes to bound the parameter uncertainty set. The algorithm is able to handle systems with bounded parameter variation between samples. It is shown that consistency checks indicating faults can be performed in a natural manner with a polytope description of the feasible parameter set. Finally, an application example is given, which demonstrates how the algorithm works on the well-known four-tank system benchmark. A comparison with a zonotope-based fault detection approach recently proposed in the literature is included.