Stability radii and spectral value sets for generalized Gershgorin perturbations

In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations ("Gershgorin type perturbations"). We derive explicit and computable formulae for the associated mu-values. The results are then applied to characterize spectral value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case the classical eigenvalue inclusion theorem of Brualdi is obtained as a corollary