Robust Stability under a Class of Nonlinear Parametric Perturbations

This paper considers the Hurwitz invariance of LTI systems under a class of nonlinear parametric perturbations. The setting is one of determining the closed loop stability of systems whose open loop transfer functions consist of powers, products and ratios of polytopes of polynomials. We give several results on the construction of value sets and Hurwitz invariance checking, for this general setting and important special cases.