Two Necessary Conditions for a Complex Polynomial to be Strictly Hurwitz and Their Applications in Robust Stability Analysis

In this note, two necessary conditions for a complex polynomial to be strictly Hurwitz (formerly available only in Chinese [1]), are reviewed and rigorously proved. Both necessary conditions have been extended to cover nonmonic polynomials instead of monic polynomials as restricted in [1], Also, based on these two results, some necessary conditions for an interval polynomial to be stable in terms of being strict Hurwitz are obtained. They can be used to quickly determine the instability of a complex interval polynomial family. Finally, their application to the study of robust stability, in the case where coefficient perturbation intervals are functions of a single parameter, is briefly discussed.