Robstness bounds of Hurwitz and Schur polynomials
The problem of robustness bounds of Hurwitz and Schur polynomials is addressed. For weighted \(L_ 2\)-norm perturbations of a Hurwitz polnomial p(s) or a Schur polynomial p(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 \textit{C. B. Soh}, \textit{C. S. Berger} and \textit{K. P. Dabke} [IEEE Trans. Autom. Control AC-30, 1033-1036 (1985; Zbl 0565.93054)]. Our approach also provides solutions for the perturbation polynomial \(\delta\) p(s) or \(\delta\) p(z) with minimal coefficient norm which cause \(p(s)+\delta p(s)\) or \(p(z)+\delta p(z)\) to be unstable.
scientific article; zbMATH DE number 4070772