This paper aims to present an approach for design of dynamic output feedback compensators for linear discrete-time descriptor systems subject to state and control constraints. To this end, output-feedback controlled-invariant polyhedra are constructed by taking a pair of polyhedral sets: a controlled-invariant set and a conditioned-invariant set. By defining an augmented system composed of the original system plus the dynamic compensator, a control action can be computed online, which optimizes the contraction rate of the augmented state trajectory and enforces the constraints. The results are illustrated through numerical examples, which show that the proposed dynamic compensators outperform static feedback controllers under the same conditions.