This paper is concerned with the flexibility in the closed loop pole location when solving the $H_2$ optimal control problem (also called the $H_2$ optimal disturbance attenuation problem) by proper measurement feedback. It is shown that there exists a precise and unique set of poles which is present in the closed loop system obtained by any measurement feedback solution of the $H_2$ optimal control problem. These “$H_2$ optimal fixed poles” are characterized in geometric as well as structural terms. A procedure...