Robust stability of linear systems relative to guarded domains

The generalized stability of families of matrices and polynomials is considered, focusing mainly on matrix families. Both one-parameter and two-parameter families of linear systems are considered. Guarding maps and semiguarding maps are introduced as a unifying tool for the study of this problem. Such maps are exhibited for a wide variety of domains of interest. Necessary and sufficient conditions for stability of one-parameter families with respect to these domains are given. In particular, a known result for Hurwitz stability of the convex hull of two matrices, as well as an analogous result for the unit disk (Schur invariance), is obtained. The two-parameter case for domains in the complex plane for which a guarding map is available is also studied