THE POLE-PLACEMENT MAP, ITS PROPERTIES, AND RELATIONSHIPS TO SYSTEM INVARIANTS

A number of new properties of the complex and real pole placement map (PPM) are derived which relate to the dimension of their images and re late them to known system invariants. It is shown that those two dimen sions are equal and that their computation is equivalent to a rank det ermination of the corresponding differential. A new expression of the differential of the PPM, allows the derivation of relationships betwee n the Markov parameters and the Plucker matrix invariant of the system . Finally, conditions for pole assignability are derived, based on the relationships between the rank of the Plucker matrix and the rank of the differential of the PPM.