A genericity result for time-varying stability radii using nonsmooth analysis

We analyze robustness bounds for linear differential inclusions on finite dimensional spaces generated by polytopes of matrices. Our results concern the question whether the exponential growth rate is strictly increasing under variation of the perturbation range, that is of the size of the polytope. Sufficient conditions for this in terms of controllability properties are provided. The basic tools in this analysis axe the Lipschitz continuity of the exponential growth rate (in the irreducible case) and the by now classical implicit function theorem for Lipschitz continuous functions.