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This paper investigates the problem of actuator fault detection filter design for discrete-time linear systems with output disturbance. By using the descriptor observer method, an H_∞ fault detection filter is designed to guarantee the residual system is admissible and satisfies the H_∞ performance. By utilizing Lyapunov function approach, a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality (LMI). The desired fault detection filter can be designed by solving a set of LMIs. Finally, a numerical example is proposed to illustrate the effectiveness of the developed method.