In this paper, the problem of output feedback stabilization of linear systems with mismatched uncertainties is investigated, A new approach to the design of output feedback controller is proposed, and the respective output feedback gains are obtained through the solution of a Riccati equation with linear constraints, Solvability conditions for such a constrained Riccati problem (CRP) are derived, and a systematic algorithm for obtaining an output feedback controller, which guarantees the system state is globally exponentially stable (GES), is provided.