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On the stability of a convex set of matrices

✍ Scribed by Vakif Dzhafarov; Taner Büyükköroğlu

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
154 KB
Volume
414
Category
Article
ISSN
0024-3795

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✦ Synopsis

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.

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