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−λ)p0(s)+λp1(s), where λ∈[0,1] and p0(s) and p1(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 λ-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.