Pole placement by static and dynamic output feedback

This paper gives new results concerning pole-assignability by static and dynamic output feedback, based on the interpretation of transfer functions, feedback laws, poles and zeroes in terms of the incidence geometry of m-planes and p-planes in (m+p)-space. As an illustration of the most basic ideas, a short proof of the Brasch-Pearson theorem is given. A more careful analysis of this proof yields a significant extension of this theorem, which is considerably sharpened in the case of pole-assignment by constant gain output feedback. As a final application, a root-locus design technique for non-square systems is introduced: zero placement by pre- or post-compensation. This zero placement problem is then analyzed by methods similar to those developed for pole placement by output feedback.