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Wirth, Fabian

The generalized spectral radius and extremal norms. (English) Zbl 0996.15020

Linear Algebra Appl. 342, No. 1-3, 17-40 (2002).
Two properties of the generalized spectral radius are establised, namely, its locally Lipschitz continuity on the space of compact irreducible sets of matrices and its strict monotonicity property. The author’s approach is based on an important idea in the analysis of exponential stability of discrete inclusions that was introduced by N. E. Barabanov [Autom. Remote Control 49, No. 2, 152-157 (1988, Zbl 0665.93043)]. The author gives a new proof for Barabanov’s result, which states that for irreducible sets of matrices an extremal norm always exists. Also, significant conditions for the existence of extremal norms are obtained.
Reviewer: Alexey Alimov (Moskva)

Cited in 2 Reviews
Cited in 70 Documents

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A18 Eigenvalues, singular values, and eigenvectors

Keywords:

generalized spectral radius; discrete inclusion; exponential stability; irreducible sets of matrices; extremal norm

Citations:

Zbl 0665.93043
Cite Review PDF
Full Text: DOI Link

References:

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