utput Feedback Pole Placement with Dynamic Compensators

Derives a new rank condition which guarantees the arbitrary pole assignability of a given system by dynamic compensators of degree at most q. By using this rank condition the authors establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system. The authors' proofs also come with a concrete numerical procedure to construct a particular compensator which assigns a given set of closed-loop poles. 830 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 41, NO. 6, JUNE 1996 utput Feedback Pole Placement with Dynamic Compensators Joachim Rosenthal, Senior Member, IEEE, and Xiaochang Alex Wang, Member, IEEE Abstract-In this paper we derive a new rank condition which guarantees the arbitrary Pole assignability of a given systemIn this paper we derive a new rank condition which guarantees the arbitrary Pole assignability of a given system rank condition we establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system. Our proofs also come with a concrete numerical procedure to construct a particular compensator which assigns a given set of closed-loop poles. can all be expressed through polynomial equations, it is not surprising that one way of studying this problem is by means of theorems available in algebraic geometry require that the field is algebraically closed, a ProPertY which the complex numbers have but the reals do not have. Still, it was possible to show through the use of the so-called dominant morphism theorem (Hermann and Martin [4]) and the use of Schubert calculus (Brockett and Bymes [SI, see also [ 2 ] ) that (3) is also a by dynamic compensators of degree at most Y * By using this algebraic geometry, Unfortunately some of the most powerful