This note considers singular systems of nonlinear differential and algebraic equations (DAEs) whose constrained state space depends on the control inputs. A state-space realization of such systems cannot be derived independently of the controller design. An output feedback pre-compensator is derived, which results in a modified DAE system whose state-space is invariant under any feedback control law and can be used for output feedback controller synthesis. Its application is illustrated by a nonlinear electrical circuit example.