Pole placement by static and dynamic output feedback

In this paper, we give new results concerning pole-assignability by static and dynamic output feed-back, based on the interpretation of transfer functions, feedback laws, poles and zeroes ([3], [5], [12], [19]) in terms of the incidence geometry of m-planes and p-planes in (m+p)-space. As an illustration of the most basic ideas, we give a short proof of the Brasch-Pearson Theorem. A more careful analysis of this proof yields a significant extension of this theorem, which we then considerably sharpen in the case of pole-assignment by constant gain output feed-back. As a final application we introduce a root-locus design technique for non-square systems: zeroplacement by pre- or post-compensation. This zeroplacement problem is then analyzed by methods similar to those developed for pole placement by output feedback.