A Gel’fand-type spectral radius formula and stability of linear constrained switching systems

Using ergodic theory, in this paper we present a Gel’fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup S+ restricted to a subset that need not carry the algebraic structure of S+ This genera...

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Bibliographic Details
Published in:Linear algebra and its applications 2012-03, Vol.436 (5), p.1099-1113
Main Author: Dai, Xiongping
Format: Article
Language:English
Subjects:
Algebra
Asymptotic stability
Exact sciences and technology
Gel’fand-type spectral-radius formula
Joint/generalized spectral radius
Linear and multilinear algebra, matrix theory
Linear switched system
Mathematics
Sciences and techniques of general use
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Summary:Using ergodic theory, in this paper we present a Gel’fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup S+ restricted to a subset that need not carry the algebraic structure of S+ This generalizes the Berger–Wang formula. Using it as a tool, we study the absolute exponential stability of a linear switched system driven by a compact subshift of the one-sided Markov shift associated to S.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2011.07.029