Design of a single-input system for specified roots using output feedback

A method is given for choosing feedbacks from an output vector of smaller dimension than the state vector in such a way that a subset of the roots assume desired values. A sufficient condition for arbitrary placement of as many roots as there are feedbacks is proved. It is also proved that a root corresponding to a mode which is either uncontrollable or unobservable cannot be altered. It may be desired to place more roots than there are feedbacks, and it is shown that the method can be extended to give an approximate solution of this problem.