On the Stability of Polynomials with Uncoupled Perturbations in the Coefficients of Even and Odd Powers.

Abstract

In this note, we present some results concerning the stability (in Hurwitz' sense) of a family of polynomials with even and odd coefficients subject to uncoupled perturbations. It is shown that the stability of an appropriate small subset of extreme polynomials guarantees the stability of the entire family. In particular, a polytope of polynomials with the even-odd uncoupling property is stable provided a certain small subset of its vertices is. For the case of an arbitrary subset of polynomials, this result gives a less conservative sufficient condition than that provided by Kharitonov's theorem.