This paper is concerned with the design of robust static and dynamic output feedback controllers for a class of uncertain linear systems with norm-bounded uncertainty. The uncertainty is assumed to enter into both the state and input matrices. However, the output matrix is assumed to be free of uncertain parameters. Necessary conditions are given for the existence of a static output feedback controller that quadratically stabilizes the system and minimizes a bound on the quadratic function. Our results may be considered as an extension of the optimal output feedback LQR problem to the case of uncertain systems with norm-bounded uncertainty. The problem of full-order and reduced-order dynamic output feedback is also considered using the static output feedback results.