Testing the robust Schur stability of a segment of complex polynomials

Given two Schur stable complex polynomials p(0)(z) and p(1)(z) of the same degree n, we present a procedure for testing if convex combinations of the form. (1-lambda )p(0)(z ) + lambdap(1)(z) are Schur stable for all lambda i s an element of [0, 1]. The procedure consists in constructing a polynomial array, which corresponds to the process of extracting the greatest common divisor of two polynomials, and testing the absence of real zeros of a real lambda polynomial of degree 2n for lambda is an element of (0, 1). Since t he latter task can be finished by using the Sturm theorem, the proposed pro cedure for testing the robust Schur stability of a segment of complex polyn omials is efficient in the sense that it accomplishes the test in a finite number of arithmetic operations. As the derivation given in this paper esta blishes a connection between our procedure and Bose's resultant method, and identifies an intrinsic simplification for the latter method, the presente d procedure can be viewed as an efficient algorithmic implementation of Bos e's resultant method for testing the robust Schur stability of complex segm ent polynomials.