The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts, in particular it characterizes the growth rate of switched linear systems. The joint spectral radius is notoriously difficult to compute and to approximate. We in...

The lower spectral radius, or joint spectral subradius, of a set of real d× d matrices is defined to be the smallest possible exponential growth rate of long products of matrices drawn from that set. The lower spectral radius arises naturally in connection with a number of topics including combinatorics on words, the stability of linear inclusions in control theory, and the study of random Cant...

We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. family of nonnegative matrices). In the case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and for finding the joint and lower spectral radii of...

For an arbitrary commuting d–tuple T of Hilbert space operators, we fully determine the spectral picture generalized spherical Aluthge transform Δt(T) and prove that radius can be calculated from norms iterates Δt(T). Let T≡(T1,…,Td) a bounded operators acting on infinite dimensional separable space, let P:=T1⁎T1+⋯+Td⁎Td, let(T1⋮Td)=(V1⋮Vd)P canonical polar decomposition, with (V1,…,Vd) (joint)...

We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger and Wang as an immediate corollary.

This article studies the constrained switching (linear) system which is a discrete-time switched linear whose sequences are by deterministic finite automaton. The stability of characterized its joint spectral radius that known to be difficult compute or approximate. Using semitensor product matrices, matrix-form expression shown equivalent lifted arbitrary system. Then, joint/generalized proven...