Plotting robust root loci for linear systems with multilinearly parametric uncertainties

This paper deals with the problem of characterizing the boundary of the image of an m-dimensional (m-D) box Q under a multilinear mapping f:R^m→C. We introduce the set of generalized principal points (GPPs) G to construct the value set f:(Q). Based on the connectedness property of GPP manifolds, we present a multidimensional pivoting procedure with integer labelling to trace out all GPP manifolds. As an application, the presented value-set construction algorithm is applied along with the zero-inclusion principle and a two-dimensional pivoting procedure to characterize the smallest set of regions in the complex plane within which all the roots of a multilinear interval polynomial family lie