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In this brief, we propose a new mixed H2/H∞ control design via a linear matrix inequality (LMI) based approach. By an equivalent transformation of Lyapunov matrix inequality, additional slack variables are introduced to characterize both the H2 and H∞ performances. Based on the characterization, a new mixed H2/H∞ control design is proposed where the introduced slack variables add in additional degree of freedom in optimizing the mixed H2/H∞ performance, resulting in equal or better performance than existing LMI based methods. The proposed control algorithm is applied in the control design for hard disk drives (HDDs) where the problem of minimizing track misregistration (TMR) in the presence of unmodeled dynamics of voice-coil motor (VCM) is formulated as a mixed H2/H∞ control problem. The simulation and implementation results of the new control design for the VCM actuator demonstrate the significant performance improvement of TMR over the existing method of while ensuring robust stability under unmodeled dynamics of VCM.