Petersen, Ian R.2026-07-022026-07-020191-2216ORCID:/0000-0003-4856-9450/work/219057282https://hdl.handle.net/1885/733812259Families of complex polynomials with coefficients lying within given intervals are considered. In particular, the problem of determining if all polynomials in a family have the property that all of their roots lie in a given region is treated. The notion of a 'Kharitonov region' is defined. 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 their roots in the region, it suffices to check only the vertex polynomials of the family. The author's main result is a sufficient condition for a given region to be a Kharitonov region.5en198710.1109/CDC.1987.2728570023604322