Robust stability of polynomials with nonlinear dependent coefficient perturbations

The robust stability of polynomial functions of interval polynomials, which is called nested polynomial families, has been investigated by Kharitonov (1996) and it can be guaranteed by checking only fixed four vertices. This paper deals with the robust stability analysis of polynomials with nonlinear uncertainty structure. For a special class of polynomial family with nonlinear dependent coefficient perturbations, some new extreme point results are obtained. We investigate the extremality properties of the inner frequency response (IFR) set associated with uncertain Hurwitz polynomials and the relationship between the stability problem of nested polynomial families and the properties of IFR set is established