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Output feedback pole assignment for transfer functions with symmetries


Helmke, U; Rosenthal, J; Wang, X (2006). Output feedback pole assignment for transfer functions with symmetries. SIAM Journal on Control and Optimization, 45(5):1898-1914.

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.
©2006 Society for Industrial and Applied Mathematics

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.
©2006 Society for Industrial and Applied Mathematics

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2006
Deposited On:11 Jan 2010 16:31
Last Modified:19 Feb 2018 06:49
Publisher:Society for Industrial and Applied Mathematics
ISSN:0363-0129
Additional Information:Copyright © 2006, Society for Industrial and Applied Mathematics
OA Status:Green
Publisher DOI:https://doi.org/10.1137/050644276
Related URLs:http://arxiv.org/abs/math/0511112

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