The robust root locus of polynomial families with multilinearparameter dependence

摘要

The mapping theorem by Zadeh and Desoer (1963) is a sufficientcondition for the zero exclusion of the image or value set of anm-dimensional box B under a multilinear mapping f :R^m→C, where R and C denote the real line and the complexplane, respectively. In this paper, we present a sufficient conditionfor the zero inclusion of the value set f( B). On the basis of these twoconditions and the iterative subdivision of the box B, we propose anumerical procedure for testing whether or not the value set f(B)includes the origin. The procedure is easy to implement and is moreefficient than that based on constructing the value set f(B) explicitly.As an application, the proposed zero inclusion test procedure is usedalong with a homotopy continuation algorithm to trace out the boundarycurves of the robust root loci of polynomial families with multilinearparametric uncertainties