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

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

2008-10-13

arxiv.org/abs/0810.2157v3

Differential Equations and Dynamical Systems, Vol. 18, Nos. 1 & 2, January & April, 2010, pp. 91-103.

Mathematics

Rings and Algebras

14 pages, 41 bibl, corrected typos, accepted to DEDS

Scientific paper

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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