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On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula

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Abstract

In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with factors taken from some matrix set plays a key role. One of the most prominent quantities characterizing the exponential rate of growth of matrix products is the so-called joint or generalized spectral radius. In the work some explicit a priori estimates for the joint spectral radius with the help of the generalized Gelfand formula are obtained. These estimates are based on the notion of the measure of irreducibility (quasi-controllability) of matrix sets proposed previously by A. Pokrovskii and the author.

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Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoj Karetny lane 19, Moscow, 127994 GSP-4, Russia

    Victor Kozyakin

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  1. Victor Kozyakin
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Dedicated to memory of Bernd Aulbach.

This work was supported by the Russian Foundation for Basic Research, projects nos. 06-01-00256, 09-01-00119.

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Kozyakin, V. On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula. Differ Equ Dyn Syst 18, 91–103 (2010). https://doi.org/10.1007/s12591-010-0010-1

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