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It is well known that a plant becomes non-minimum phase in discrete-time domain when the relative degree of the original continuous-time plant is greater than 2 even if the plant is minimum-phase in continuous-time domain. Thus, it was difficult to apply the conventional adaptive controllers directly to these systems. In this paper, multirate adaptive robust control (MARC) is proposed for these systems. This scheme is developed by the good combination of perfect tracking control (PTC) with multirate feedforward control which has been proposed by the first author and discontinuous projection based adaptive robust control (ARC) which has been proposed by the second author. Although the original PTC can assure perfect tracking only for nominal plant, the proposed MARC can guarantee: 1) perfect tracking for plant with parametric uncertainty and 2) overall stability even if there exist modeling error and disturbance. The proposed scheme is applied to the high-speed position control of a linear motor, and the advantages are demonstrated through experiments.