A test for robust Hurwitz stability of convex combinations of complex polynomials

In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1 - lambda)p(o)(s) +lambdapl(s), where lambdais an element of[0, 1] and p(o)(s) and p(l)(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real lambda-polynomials of degrees 2 and 2n in the interval (0, 1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure. (C) 2002 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.