On the stability of a convex set of matrices

Dzhafarov V., Buyukkoroglu T.

LINEAR ALGEBRA AND ITS APPLICATIONS, cilt.414, sa.2-3, ss.547-559, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 414 Sayı: 2-3
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.laa.2005.10.044
  • Dergi Adı: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.547-559
  • Anahtar Kelimeler: stability, constant inertia, minimax theorem, companion matrix, NP-HARD, LYAPUNOV, INERTIA, CONES
  • Anadolu Üniversitesi Adresli: Hayır

Özet

In this paper we give an alternative proof of the constant inertia theorem for convex compact sets of complex matrices. It is shown that the companion matrix whose non-trivial column is negative satisfies the directional Lyapunov condition (inclusion) for real multiplier vectors. An example of a real matrix polytope that satisfies the directional Lyapunov condition for real multiplier vectors and which has nonconstant inertia is given. A new stability criterion for convex compact sets of real Z-matrices is given. This criterion uses only real vectors and positive definite diagonal matrices. (c) 2005 Elsevier Inc. All rights reserved.