The influence of state feedback on the transfer matrix in singular systems is considered. We first discuss the problem for SISO systems, then by utilizing the time-scale transformation the same problem is solved for MIMO systems. We also consider realizations of the feedback control strategies given here. It is pointed out that the singular system is distinguished from the normal one by an important feature: we can design a pure input prediction system for it. Finally, the results are applied to the model matching problem.