This work addresses the derivation of state-space realizations for the output feedback control of linear, high-index differential-algebraic-equation systems that are not controllable at infinity and for which the control inputs appear explicitly in the underlying algebraic constraints. The constrained state space of such systems depends on the control inputs, and thus, a state-space realization cannot be derived independently of the controller design. Motivated by this, initially a dynamic output feedback compensator is designed that yields a modified system for which the algebraic constraints are independent of the new control inputs. For this feedback modified system, a state-space realization is then derived which can be used for output feedback controller synthesis.