  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.
