Pole placement results for complex symmetric and Hamiltonian transfer functions

U. Helmke, J. Rosenthal, X. Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages3450-3453
Number of pages4
DOIs
StatePublished - Dec 1 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

    Fingerprint

Keywords

  • Degree of a projective variety
  • Inverse eigenvalue problems
  • Lagrangian grassmannian
  • Output feedback
  • Pole placement
  • Symmetric or hamiltonian realizations

Cite this

Helmke, U., Rosenthal, J., & Wang, X. (2007). Pole placement results for complex symmetric and Hamiltonian transfer functions. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 3450-3453). [4435047] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4435047