Bezoutians

U. Helmke, P. A. Fuhrmann

Research output: Contribution to journalArticlepeer-review

71 Scopus citations

Abstract

We survey the theory of Bezoutians with a special emphasis on its relation to system theoretic problems. Some instances are the connections with realization theory, in particular signature symmetric realizations, the Cauchy index, stability, and the characterization of output feedback invariants. We describe canonical forms and invariants for the action of static output feedback on scalar linear systems of McMillan degree n. Previous results on this subject are obtained in a new and unified way, by making use of only a few elementary properties of Bezout matrices. As new results we obtain a minimal complete set of 2n-2 independent invariants, an explicit example of a continuous canonical form for the case of odd McMillan degree, and finally a canonical form which induces a cell decomposition of the quotient space for output feedback.

Original languageEnglish
Pages (from-to)1039-1097
Number of pages59
JournalLinear Algebra and Its Applications
Volume122-124
Issue numberC
DOIs
StatePublished - 1 Jan 1989

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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