In 2002 F. Wirth has proved that the joint spectral radius of irreducible compact sets of matrices is locally Lipschitz continuous as a function of the matrix set. In the paper, an explicit formula for the related Lipschitz constant is obtained. PACS number 02.10.Ud; 02.10.Yn MSC 2000: 15A18; 15A60

In 2002 F. Wirth has proved that the joint spectral radius of irreducible compact families of matrices is locally Lipshitz continuous as a function of the matrix family. In the paper, an explicit formula for the related Lipshitz constant is obtained. PACS number 02.10.Ud; 02.10.Yn MSC 2000: 15A18; 15A60

We consider discrete-time homogeneous systems under arbitrary switching and study their growth rate, the analogue of joint spectral radius for switched linear systems. We show that a system is asymptotically stable if and only if its growth rate is less than unity. We also provide an approximation algorithm to compute growth rate to an arbitrary accuracy.

We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale’s linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of WFA plays a central role. We also study continui...

The ε-pseudospectral abscissa and radius of an n × n matrix are respectively the maximal real part and the maximal modulus of points in its ε-pseudospectrum, defined using the spectral norm. Existing techniques compute these quantities accurately but the cost is multiple singular value decompositions and eigenvalue decompositions of order n, making them impractical when n is large. We present n...

We recast the notion of joint spectral radius in setting groups acting by isometries on non-positively curved spaces and give geometric versions results Berger–Wang Bochi valid for δ-hyperbolic symmetric non-compact type. This method produces nice hyperbolic elements many classical settings. Applications to uniform growth are given, particular a new proof generalization theorem Besson–Courtois–...