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This paper describes a new method for detecting sensor faults using sliding mode observers. In general, required capabilities of FDI(Fault Detection and Isolation) filters are sensitivity of occurring faults and robustness against disturbances. A FDI filter that proposed in this paper can estimate faults even if disturbances exist. Moreover, we discretize continuous-time FDI filters into discrete-time FDI filters using difference equations and apply the FDI filter to a vibration experimental system. An example demonstrates the effectiveness of the proposed method in comparison with conventional methods.