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A new covariance based formulation of the actuator selection problem is presented. The proposed optimization problem is aimed at finding the set of minimum cost actuator arrays such that there exists a linear feedback for which all closed-loop signals will satisfy pre-specified variance bounds. Through a linear matrix inequality (LMI) based transformation we exactly convert the original problem into a computationally attractive mixed integer convex program (MICP). The resulting MICP leads to the first computational scheme capable of calculating globally optimal solutions to the covariance based actuator selection problem. It is further shown that the formulation is general enough to incorporate extensions to the actuator noise and actuator dynamics cases. Finally, a set of examples are presented to illustrate the scheme as well as the scalability of required computational effort.