A class of stability regions for which a Kharitonov like theorem holds

This paper deals with families of complex polynomials whose coefficients lie within given intervals. In particular, the paper is concerned with the problem of determining if all polynomials in a family have the property that all of their roots lie in a given region. Towards this end, the paper defines a notion of a "Kharitonov Region". Roughly speaking a Kharitonov region is a region in the complex plane with the following property: Given any suitable family of polynomials, in order to determine if all polynomials in the family have all of their roots in the region, it suffices to check only the vertex polynomials of the family. The main result of this paper is a sufficient condition for a given region to be a Kharitonov region.