A novel approach for finding stabilizing static output feedback (SOF) for continuous-time linear time-invariant systems has been addressed. We explore conditions on the structure of generalized plants under which necessary and sufficient conditions for the existence of stabilizing SOF gains are derived in terms of linear matrix inequalities (LMIs). Extension to some other control performances is made in a unified manner. The optimal H-infinity (or H2) gains can be efficiently computed via convex optimization. Numerical examples are given for illustration.