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Pole placement and matrix extension problems: a common point of view


Kim, M; Rosenthal, J; Wang, X (2004). Pole placement and matrix extension problems: a common point of view. SIAM Journal on Control and Optimization, 42(6):2078-2093.

Abstract

This paper studies a general inverse eigenvalue problem which generalizes many well-studied pole placement and matrix extension problems. It is shown that the problem corresponds geometrically to a so-called central projection from some projective variety. The degree of this variety represents the number of solutions the inverse problem has in the critical dimension. We are able to compute this degree in many instances, and we provide upper bounds in the general situation.

Abstract

This paper studies a general inverse eigenvalue problem which generalizes many well-studied pole placement and matrix extension problems. It is shown that the problem corresponds geometrically to a so-called central projection from some projective variety. The degree of this variety represents the number of solutions the inverse problem has in the critical dimension. We are able to compute this degree in many instances, and we provide upper bounds in the general situation.

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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
Uncontrolled Keywords:pole placement and inverse eigenvalue problems, matrix completion problems, Grassmann varieties, degree of a projective variety
Language:English
Date:2004
Deposited On:11 Mar 2010 09:01
Last Modified:21 Nov 2017 14:21
Publisher:Society for Industrial and Applied Mathematics
ISSN:0363-0129
Additional Information:©2004 Society for Industrial and Applied Mathematics
Publisher DOI:https://doi.org/10.1137/S0363012999354429

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