This paper proposes a robust track-following controller design method for a dual-stage servo system in magnetic hard disk drives (HDDs). The method formulates the problem of minimizing track misregistration (TMR) in the presence of plant uncertainty and variation as a multiobjective optimization problem. Tracking error minimization is naturally formulated as an$H_2$norm minimization problem, while the robust stability issue is addressed by some$H_infty$norm bounds. This mixed$H_2/H_infty$control problem can then be formulated as a set of linear matrix inequalities (LMIs) and be efficiently solved through convex optimization algorithms. To enhance the system's tracking performance and stability robustness, the method explicitly takes attenuation of airflow-excited suspension vibration into consideration by an inner loop fast rate damping and compensation controller that utilizes the output of a strain gauge sensor on the suspension surface. Analysis and simulation show that a system designed by this method can achieve good tracking performance while still keeping stability robustness to plant variation and high-frequency spillover.