Robustness bounds of Hurwitz and Schur polynomials

In this paper, the problem of robustness bounds of Hurwitz and Schur polynomials is addressed. For weightedL ₂-norm perturbations of a Hurwitz polynomialp(s) or a Schur polynomialp(z), a new method is developed for calculating the maximal perturbation bound under which stability is preserved. We show that such a robustness bound is related to the minimum of a rational function. The new method is superior to the previous one developed by Soh, Berger, and Dabke in Ref. 1. Our approach also provides solutions for the perturbation polynomial p(s) or p(z) with minimal coefficient norm which causep(s)+p(s) orp(z)+p(z) to be unstable.