An explicit Lipschitz constant for the joint spectral radius

Abstract

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.

9 pages, corrected typos and references

References in corpus (5)

• Approximation of the joint spectral radius using sum of squares
• Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets
• Estimates of Amplitudes of Transient Regimes in Quasi-Controllable Discrete Systems
• Quasi-Controllability and Estimates of Amplitudes of Transient Regimes in Discrete Systems
• On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula

Cited by in corpus (10)

• Mather sets for sequences of matrices and applications to the study of joint spectral radii
• The Berger-Wang formula for the Markovian joint spectral radius
• Continuity properties of the lower spectral radius
• The joint spectrum
• Bisimulation Metrics for Weighted Automata
• Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems
• Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations
• The joint spectral radius is pointwise Hölder continuous
• Continuous products of matrices
• On the spectral radius of compact operator cocycles