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An inequality for the spectral radius of an interval matrix. (English) Zbl 0915.15017

The main result of this paper says that for each square interval matrix \({\mathbb A}\) a real matrix \(A\) with the property \[ \rho({\mathbb A})\leq\rho(A) \] can be constructed, where \(\rho\) on the right-hand side stands for the spectral radius whereas on the left-hand one it denotes the generalized spectral radius in the sense of I. Daubechies and J. C. Lagarias [Linear Algebra Appl. 161, 227-263 (1992; Zbl 0746.15015)]. Further it is proved that \[ \rho({\mathbb A})=\rho(\text{ext} {\mathbb A}), \] where \(\text{ext} {\mathbb A}\) is the set of vertices of \({\mathbb A}\). Application of these results to checking asymptotic stability of discrete time-varying linear systems is considered.
Reviewer: J.Rohn (Praha)

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
65G30 Interval and finite arithmetic
93D20 Asymptotic stability in control theory

Citations:

Zbl 0746.15015
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References:

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