Generation of robust root loci for linear systems with parametric uncertainties in an ellipsoid

Given a parametric polynomial family p. s; Q): = {Sigma (n)(k=0) a(k)(q)s(k ) : q is an element of Q}, Q subset of R-m, the robust root locus of p(s; Q ) is defined as the two-dimensional zero set Pi (p,Q) := {s is an element o f C: p(s; q) = 0 for some q is an element of Q}. In this paper we are conce rned with the problem of generating robust root loci for the parametric pol ynomial family p(s; E) whose polynomial coefficients depend polynomially on elements of the parameter vector q is an element of E which lies in an m-d imensional ellipsoid E. More precisely, we present a computational techniqu e for testing the zero inclusion/exclusion of the value set p(z; E) for a f ixed point z in C, and then apply an integer-labelled pivoting procedure to generate the boundary of each subregion of the robust root locus Pi (p,E). The proposed zero inclusion/exclusion test algorithm is based on using som e simple sufficient conditions for the zero inclusion and exclusion of the value set p(z, E) and subdividing the domain E iteratively. Furthermore, an interval method is incorporated in the algorithm to speed up the process o f zero inclusion/exclusion test by reducing the number of zero inclusion te st operations. To illustrate the effectiveness of the proposed algorithm fo r the generation of robust root locus, an example is provided.