%0 Journal Article
%T On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula
%A Victor Kozyakin
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0810.2157v3