In conventional hard disk drives, a control system compensates the mechanical resonance by using a multi-rate notch filter that can decrease the gain above the nyquist frequency. However, such a control system (which is based on the small-gain theorem) only avoids becoming unstable by mechanical resonances. It cannot suppress the vibrations caused by these resonances. In response to these problems, we proposed a design method for a sampled-data control system that uses frequency responses of a controlled object and a digital controller. Our method can calculate the norm of the sensitivity function in a sampled-data system and design a control system that decreases vibrations that occur at frequencies above the nyquist frequency. When the method was applied to the head-positioning system of a hard disk drive, we found that a mechanical resonance, in which the frequency was above the nyquist frequency, could be stabilized by the phase condition, and the vibrations could be decreased by the control system