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.

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

References in corpus (3)

• Approximation of the joint spectral radius using sum of squares
• Inequalities for numerical invariants of sets of matrices
• Estimates of Amplitudes of Transient Regimes in Quasi-Controllable Discrete Systems

Cited by in corpus (3)

• On accuracy of approximation of the spectral radius by the Gelfand formula
• An explicit Lipschitz constant for the joint spectral radius
• Sequences of Arbitrages