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

Meeyoung Kim, Joachim Rosenthal, Xiaochang Alex Wang

Research output: Contribution to journalArticle

10 Scopus citations

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.

Original languageEnglish
Pages (from-to)2078-2093
Number of pages16
JournalSIAM Journal on Control and Optimization
Volume42
Issue number6
DOIs
StatePublished - 2004

Keywords

  • Degree of a projective variety
  • Grassmann varieties
  • Matrix completion problems
  • Pole placement and inverse eigenvalue problems

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