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We present several results describing the interplay between the max algebraicjoint spectral radius (JSR) for compact sets of matrices and suitably definedmatrix norms. In particular, we extend a classical result for the conventionalalgebra, showing that the JSR can be described in terms of induced norms of thematrices in the set. We also show that for a set generating an irreduciblesemigroup (in a cone-theoretic sense), a monotone Barabanov norm always exists.This fact is then used to show that the max algebraic JSR is locally Lipschitzcontinuous on the space of compact irreducible sets of matrices with respect tothe Hausdorff distance. We then prove that the JSR is Hoelder continuous on thespace of compact sets of nonnegative matrices. Finally, we prove a strictmonotonicity property for the max algebraic JSR that echoes a fact for theclassical JSR.

Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius