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This paper considers robust fault detection and diagnosis for input uncertain nonlinear systems. It proposes a multi-objective fault detection criterion so that the fault residual is sensitive to the fault but insensitive to the uncertainty as much as possible. Then the paper solves the proposed criterion by maximizing the smallest singular value of the transformation from faults to fault detection residuals while minimizing the largest singular value of the transformation from input uncertainty to the fault detection residuals. This method is applied to an aircraft which has a fault in the left elevator or rudder. The simulation results show the proposed method can detect the control surface failures rapidly and efficiently.