An explicit Lipschitz constant for the joint spectral radius

TL;DR

This paper derives an explicit formula for the Lipschitz constant of the joint spectral radius, enhancing understanding of its stability and sensitivity to changes in matrix sets.

Contribution

The paper provides a new explicit formula for the Lipschitz constant of the joint spectral radius for irreducible compact matrix sets.

Findings

Explicit Lipschitz constant formula derived

Improved understanding of joint spectral radius stability

Potential applications in control theory and matrix analysis

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.