Value sets of polynomial families with coefficients depending nonlinearly on perturbed parameters

In this paper, we consider the problem of constructing the value set of an m-dimensional box Q under a nonlinear differentiable mapping f:R^m→C, where R and C denote the sets of real and complex numbers, respectively. More precisely, we present an effective procedure for obtaining the set of generalized principal point (GPP) G whose image covers the boundary of the value set f(Q). As a specific application, the proposed value-set construction procedure is utilized for the robust D-stability analysis of a family of polynomials whose coefficients depend nonlinearly on perturbed parameters, without gridding the boundary of the region D