TY - GEN

T1 - Pole placement results for complex symmetric and Hamiltonian transfer functions

AU - Helmke, U.

AU - Rosenthal, J.

AU - Wang, X.

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2007

Y1 - 2007

N2 - This paper studies the problem of pole assignment for symmetric and Hamiltonian transfer functions. A necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given. Moreover, in the case where the McMillan degree coincides with the number of parameters appearing in the symmetric feedback transformations, we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains. The proof uses intersection theory in projective space as well as a formula for the degree of the complex Lagrangian Grassmann manifold.

AB - This paper studies the problem of pole assignment for symmetric and Hamiltonian transfer functions. A necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given. Moreover, in the case where the McMillan degree coincides with the number of parameters appearing in the symmetric feedback transformations, we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains. The proof uses intersection theory in projective space as well as a formula for the degree of the complex Lagrangian Grassmann manifold.

KW - Degree of a projective variety

KW - Inverse eigenvalue problems

KW - Lagrangian grassmannian

KW - Output feedback

KW - Pole placement

KW - Symmetric or hamiltonian realizations

UR - http://www.scopus.com/inward/record.url?scp=62749188813&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4435047

DO - 10.1109/CDC.2007.4435047

M3 - Conference contribution

AN - SCOPUS:62749188813

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3450

EP - 3453

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -