A desirable property of an optimal system with full state feedback was shown by Kalman to be satisfaction of a circle condition in the A(jw) plane where A(s) is the loop gain function (return ratio) of the optimal system. This thesis demonstrates that this same property is satisfied by systems which are designed to be optimal using output feedback. The implications of this result are applied to the problem of system stability in the presence of a time-varying, nonlinear gain at the plant input. This thesis also investigates the optimality of dual mode control for systems using output feedback.