This note presents a new approach for the robustness of Hurwitz polynomials under coefficient perturbation. The s-domain Hurwitz polynomial is transformed to the z-domain polynomial by the bilinear transformation. Then an approach based on the Rouché theorem introduced in the literature is applied to compute a crude bound for the allowable coefficient variation such that the perturbed polynomial maintains the Hurwitz stability property. Three methods to obtain improved bounds are also suggested. The results of this note are computationally more efficient than the existing direct s-domain approaches especially for polynomials of higher degree. Furthermore examples indicate that the exact bound for the coefficient variation can be obtained in some cases.

New equivalent characterizations are derived for Schur stability property of real polynomials. They involve a single scalar parameter, which can be regarded as a freedom incorporated in the given polynomials so long as the stability is concerned. Possible applications of the expressions are suggested to the latest results for stability robustness analysis in parameter space. Further, an extension of the characterizations is made to the matrix case, yielding one-parameter expressions of Schur matrices.