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An observer-based fault detection direct design method for multirate sampled-data systems (MSD) is investigated in this paper. Firstly, by use of the discrete lifting technique, the MSD fault detection problem is transformed into an equivalent slow rate pure discrete time problem based on the Hinfin optimal direct design method of single rate sampled-data systems. An Hinfin performance index is then optimized to make the obtained residuals sensitive to the faults and robust to the unknown inputs. An extend QR decomposition algorithm is put forward to ensure the residual generator satisfying the causality constraints. Finally the residual is inverse lifted to implement fast rate fault detection. Simulation results of a numerical example are provided to illustrate the efficiency of the proposed approach.