This paper considers the problem of designing dynamic compensators for linear multivariable systems to obtain arbitrary pole placement while minimizing a quadratic performance index in the system state and control variables. The design employs feedback from only the available system outputs. A static optimization problem in the compensator parameters is formulated, the solution of which, using the algorithm derived in the paper, yields the required design. Unlike in the work of Brasch and Pearson (1970) and other authors, no unity-rank constraints are imposed on any of the compensator matrices. Consequently, pole placement is obtained with compensators that are often of lower order than required by them.