Hasse Diagram and Dynamic Feedback of Linear Systems

The output feedback pole placement problem of linear systems with static or dynamic compensators belongs to the classical problems in control theory and many theoretical and numerical research papers were already devoted to this problem. Although the considered systems are linear, the problem requires the solution of an over determined system of quadratic polynomial equations. A lot of progress has been made on the static feedback problem. It was Brockett and Byrnes [1] who explained first the pole placement problem with static compensators as an intersection problem in a compactified set of static compensators, the Grassmannian Grass(p,m+ p). In making the connection to the classical Schubert calculus they were able to show that there are