On the stability of a convex set of matrices

Dzhafarov V., Buyukkoroglu T.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.414, no.2-3, pp.547-559, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 414 Issue: 2-3
  • Publication Date: 2006
  • Doi Number: 10.1016/j.laa.2005.10.044
  • Journal Name: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.547-559
  • Keywords: stability, constant inertia, minimax theorem, companion matrix, NP-HARD, LYAPUNOV, INERTIA, CONES
  • Anadolu University Affiliated: No

Abstract

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.