Maximal perturbation bound for perturbed polynomials with roots inthe left-sector

摘要

Considers the problem of computing the largest perturbation bounds for a perturbed polynomial while simultaneously maintaining the correct number of zeros in the left-sector. The uncertain polynomial coefficients are assumed to be described by either the interval bound or the 1-norm bound. The authors show that the largest allowable perturbation bound for the nominal polynomial can be obtained by computing the minimum distance of the Nyquist image of the perturbed polynomial from the origin of the complex plane. The proposed algorithms are frequency-domain based and can be computed efficiently