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In various problems of control theory, non-autonomous and multivalueddynamical systems, wavelet theory and other fields of mathematics informationabout the rate of growth of matrix products with factors taken from some matrixset plays a key role. One of the most prominent quantities characterizing theexponential rate of growth of matrix products is the so-called joint orgeneralized spectral radius. In the work some explicit a priori estimates forthe joint spectral radius with the help of the generalized Gelfand formula areobtained. These estimates are based on the notion of the measure ofirreducibility (quasi-controllability) of matrix sets proposed previously by A.Pokrovskii and the author.

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