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This paper investigates the disturbance rejection problem for a data storage servo system that contains a microactuator for high-accuracy positioning. For disturbances with known frequencies, their rejection is accomplished via the generalized Kalman-Yakubovic-Popov lemma together with the Youla parameterization approach, and a linear controller is computed via solving a number of linear matrix inequalities. To further improve the rejection of low-frequency disturbances such as nonlinear disturbances arising from friction torque or bias or other unknown disturbances, an adaptive nonlinear compensation scheme is adopted to cancel their effects on the positioning accuracy. Simulation together with implementation results demonstrate that the proposed design offers a remarkably improved positioning accuracy.