Abstract: Based on linear matrix inequality(LMI),the problem of H_∞ fault detection for Delta operator-formulated discrete-time system is studied.The fault and the disturbance are regarded as the generalized disturbances.By using H_∞ control theory,sufficient conditions for the existence of the H_∞ fault detection filter for Delta operator-formulated discrete-time system are given in LMI forms.Then a numerical example is given to illustrate the effectiveness of the proposed approach.The designed filter can ensure that the resulted closed-loop Delta operator-formulated system is asymptotically stable and has the expected H_∞ performance,and the fault detection results are closer to the results which are based on continuous systems when the sampling period is very small.