When is the Multiaffine Image of a Cube a Polygon?

Abstract

We give two simple sufficient conditions under which the multiaffine image on the complex plane of an m-dimensional cube is a convex polygon. A third condition which, in some generic sense, is necessary and sufficient is then obtained. The conditions involve checking the locations of the image of the vertices of the cube. These results help determine whether a family of parametrized polynomials is stable, and provide a tool for robust control analysis.