For the purpose of the incipient fault dignosis under disturbances with unknown upper bound, a fault diagnosis method based on the synthetical unknown input observer is put forward, which not only can detect and estimate the incipient sensor fault, but also is robust to disturbances. First, the original system is decoupled into two subsystems by coordinate transformation such that one has only the incipient sensor fault which is detected and estimated by observers and the other has only the disturbance which is eliminated by the unknown input observer, and the constraint conditions of gain matrices are reduced. Then, the stability of the error dynamics is proven by the Lyapunov function and is expressed in the form of linear matrix inequality. Finally, the proposed method is applied to the motor systems and the simulation results show the effectiveness of the proposed method.