This paper presents the discrete-time counterpart of a PI-like output feedback tracking controller recently proposed for linear continuous-time systems subject to state and input constraints. The considered approach exploits the internal model principle to design via robust positive invariance and the Extended Farkas' Lemma, a constrained set-point tracking controller. The polyhedral setup allows a bilinear optimization design problem that simultaneously determines the sets of admissible set-points and the plant's initial conditions. The proposal guarantees asymptotic offset-free set-point tracking, local stability, and constraint fulfillment. Simulation results show the design's effectiveness.