This paper deals with the optimal output feedback problem of how to initialize a controller's state when the initial value of the system is known. Special attention is paid to a tracking problem. Owing to the design freedom of the controller's initial state, there exist optimal controllers to recover the optimal performance that a state feedback law can attain. Other advantages with our optimal controllers are the requisite internal model and an invariance property, which shows that the assignment of a controller's dynamic parameters is independent of the system's initial state.