Explicit formulas for stability radii of nonnegative and Metzlerian matrices

We address stability issues pertaining to uncertain nonnegative and Metzlerian matrices. The problem under consideration is the computation of the stability radius when matrix perturbations are both unstructured and structured. We show that the stability radius can be obtained in the former case by computing the largest singular value of a constant matrix and in the latter case by computing the spectral radius of a constant matrix.