An Enestrom-Kakeya theorem for Hermitian polynomial matrices

We extend the Enestrom-Kakeya theorem and its refinement by Hurwitz to polynomial matrices H(z) with positive semidefinite coefficients. We determine an annular region containing the zeros of det H(z). A stability result for systems of linear difference equations is given as an application. Index Terms--Block companion matrix, Enestrom-Kakeya theorem, polynomial matrices, root location, system of difference equations, zeros of polynomials.