The problem of obtaining output feedback gains to minimize a quadratic performance criterion which includes sensitivity variables is discussed. The equivalent stochastic problems are also studied and when a Kalman filter is allowed, the minimum variance estimate of the state is employed to implement the control. A set of non-linear matrix equations are obtained which constitute the necessary conditions that must be satisfied for an optimal solution. For the deterministic case it is shown that when no sensitivity is considered and the matrix which relates output and input is invertible, the usual Riccati formulation is obtained. The problem is also reformulated using a compensator and it is shown that it can be cast into an instantaneous feedback form.