We have developed an analysis and synthesis method for mixed-sensitivity problems in sampled-data positioning control systems. The method uses frequency responses of the controlled object and the digital controller for calculating the characteristics of the control system without complicated calculations involving matrices. Our proposed method indicates relationships between the sensitivity function and complementary sensitivity function for the mixed sensitivity problem in a sampled-data positioning control system. We also address the mixed sensitivity problem for multi-rate control systems that include an interpolator, a multi-rate filter, and a multi-rate hold. To show the validity of the proposed method, we conducted simulations and experiments on the sampled-data positioning control system of a head-positioning control system in a hard disk drive. These results show that control engineers should know the difference between the discrete-time control system and the sampled-data control system even for frequencies below the Nyquist frequency.