On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula
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.
Keywords
Cite
@article{arxiv.0810.2157,
title = {On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula},
author = {Victor Kozyakin},
journal= {arXiv preprint arXiv:0810.2157},
year = {2010}
}
Comments
14 pages, 41 bibl, corrected typos, accepted to DEDS