The C-numerical range of perturbations matrix polynomials

Abstract

In this paper, the [Formula: see text]-radius stability of a matrix polynomial [Formula: see text] relative to a domain [Formula: see text] of the complex plane and its relation with the [Formula: see text]-numerical range of [Formula: see text] are investigated. By using an expression of the [Formula: see text]-radius stability, we obtain a lower bound which involves the distance of [Formula: see text] from the connected components of the [Formula: see text]-numerical range of [Formula: see text].