The use of optimal control tracking methodologies for the development of feedback control schemes for arbitrary discrete-time linear systems is considered for the special case when the demand signal is multi-periodic, i.e. can be expressed as a finite sum of periodic signals of different but known frequencies. By embedding the reference signal into plant dynamics, the problem is reduced to a classical linear quadratic control problem which yields an explicit formula for a globally stabilizing tracking controller. Asymptotic perfect tracking is guaranteed by the presence of the familiar internal model of the demand signal dynamics within the control structure. Transfer function analysis of the controller indicates that it consists of an inner state feedback loop plus an error actuated forward path control element containing the internal model.