On the stability of a convex set of matrices
LINEAR ALGEBRA AND ITS APPLICATIONS, vol.414, no.2-3, pp.547-559, 2006 (SCI-Expanded, Scopus)
- 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.