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In this paper, we develop a covariance control problem to address a tradeoff between H 2 performance and H ∞ disturbance attenuation. In particular, we formulate a mixed-norm H 2 / H ∞ and entropy covariance control problem that guarantees that the state covariance of an uncertain dynamical system driven by white noise is upper bounded in the sense of the cone of nonnegative definite matrices by a given threshold matrix via state feedback as well as output feedback control. This is accomplished by combining H 2 covariance control theory and mixed norm H 2 / H ∞ control theory. By using suitable transformations involving dynamic weighting on the complimentary sensitivity system transfer function, the proposed formulation is applicable to robustness problems involving nominal performance subject to a robust stability requirement. The proposed formulation allows for solutions via semidefinite programming. Finally, two illustrative numerical examples are provided to show the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]