Schur's Theorem on the Stability of Networks

Abstract

A complex polynomial is called a Hurwitz polynomial if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical networks. In this article we prove Schur's criterion [17] that allows to decide whether a polynomial p(x) is Hurwitz without explicitly computing its roots: Schur's recursive algorithm successively constructs polynomials p_i(x) of lesser degree by division with x - c, Re(c) < 0, such that p_i(x) is Hurwitz if and only if p(x) is.