This paper considers the problem of the optimal control of a linear servomechanism using output feedback. It is shown that a generalization of the standard optimal control problem can be obtained in such a manner that optimal control is possible by feeding system outputs into a dynamic controller which operates only on past and present values of these outputs. This represents a new approach to the design of controllers for linear systems which may play an important role in applications of optimal control theory. It allows the linear servomechanism problem to be treated, for the first time, in a realistic manner.