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Pole placement results for complex symmetric and Hamiltonian transfer functions


Helmke, U; Rosenthal, J; Wang, X (2007). Pole placement results for complex symmetric and Hamiltonian transfer functions. In: Parisini, T. Proceedings of the 46th IEEE Conference on Decision and Control. New Orleans: IEEE, 3450-3453.

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.

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.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:11 Dec 2009 08:03
Last Modified:05 Apr 2016 13:23
Publisher:IEEE
ISBN:978-1-4244-1497-0
Additional Information:46th IEEE Conference on Decision and Control, New Orleans, LA, DEC 12-14, 2007
Publisher DOI:https://doi.org/10.1109/CDC.2007.4435047

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