A stabilization criterion for matrix pencils under bilinear transformation

Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos, Athanasios A. Pantelous

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9 Citations (Scopus)


In the literature, the dual matrix pencils sF - G and F - over(s, ̂) G are identified with the homogeneous pencil sF - over(s, ̂) G. In the present paper, for a given a homogeneous pencil which is unstable, in the sense that it has roots in the closed right half-plane, a bilinear transformation is determined such that the new homogeneous bilinear-equivalent matrix pencil is stable. The notion of bilinear equivalence is introduced and a stabilization criterion of a homogeneous matrix pencil is finally derived.

Original languageEnglish
Pages (from-to)2852-2862
Number of pages11
JournalLinear Algebra and Its Applications
Issue number11-12
Publication statusPublished - 1 Jun 2008
Externally publishedYes


  • Bilinear equivalence
  • Elementary divisors
  • Linear systems
  • Matrix pencil
  • Stability

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