On robust eigenvalue configuration

This study focuses on a class of disconnected subsets of the complex plane, of interest in the context of dominant pole assignment and filter design. It is first observed that the robust stability conditions originally put forth are in fact necessary and sufficient for the number of eigenvalues (matrices) or zeros (polynomials) in any given connected component to be the same for all the members of the given family. Polynomic semiguardian maps are then identified for a class of disconnected regions of interest. These maps are in fact essentially guarding with respect to one-parameter families