The use of Routh array for testing the Hurwitz property of a segment of polynomials

In this paper we show that the test of Hurwitz property of a segment of pol ynomials (1 - lambda )p(0)(s) + lambdap(1)(s), where lambda is an element o f [0,I], p(0)(s) and p(1)(s) are nth-degree polynomials of real coefficient s, can be achieved via the approach of constructing a fraction-free Routh a rray and using Sturm's theorem. We also establish the connection between th e proposed approach and the finite-step methods based on the resultant theo ry and the boundary crossing theorem. In a certain sense, the proposed appr oach provides an efficient numerical implementation of the later two method s and, therefore, by which the robust Hurwitz stability of convex combinati ons of polynomials can be checked in a definitely finite number of arithmet ic operations without having to invoke any root-finding procedure. (C) 2000 Elsevier Science Ltd. All rights reserved.