A necessary and sufficient condition for state feedback implementing by output feedback

State feedback is the feedback of complete information being hold, and it can come to pole arbitrary placement under the condition of that (A,B) is controllable pair, therefore it can hold closed-loop stability. In another way, the system should come to the same function by output feedback under the information can not get completely or the state is not detectable, because the equation of FC=K did not have the solution F in any condition. We give a necessary and sufficient condition for state feedback implementing by output feedback. We studied deeply and inducted the conception of general inverse, and put it to a example of optimal output regulator. It proved that our theory is correct and valid.