Summary: For the linear systems with unknown but bounded noises, set membership algorithm based on convex polytope is used to complete fault diagnosis. Set membership filters are designed according to different faults, solving the state feasible set of the set membership filter based on the normal model, and checking whether or not it is empty to finish fault detection. At the same time, a way of “model falsification” is used to accomplish fault isolation, which is aiming to find the only set membership filter that is not null. The simulation analysis shows the feasibility of the proposed method for different types of fault diagnosis.