Closed-loop performance properties of a large flexible space structure with colocated actuators and sensors are examined. It is shown that when an output feedback gain matrix is chosen as symmetric negative-definite, a linear quadratic optimization (LQ) problem can be stated and solved in closed form via an inverse optimal control formulation. The known properties of this LQ problem guarantees the stability of the closed-loop system. It is further shown that the closed-loop system remains stable in the presence of certain parameter variations. These robustness properties include also the effect of truncated modes on stability. The understanding of the specific output feedback controller, offered through the inverse optimal control solution, lends itself to a design procedure that selects the output feedback gain matrix in an iterative manner.