Stable Factorization of Strictly Hurwitz Polynomials
Keywords:Routh-Hurwitz stability, Hurwitz polynomial, stable factorization, Newtonâ€™s method
AbstractWe propose a stable factorization procedure to generate a strictly Hurwitz polynomial from a given strictly positive even polynomial. This problem typically arises in applications involving real frequency techniques. The proposed method does not require any root finding algorithm. Rather, the factorization process is directly carried out to find the solution of a set of quadratic equations in multiple variables employing Newton’s method. The selection of the starting point for the iterations is not arbitrary, and involves interrelations among the coefficients of the set of solution polynomials differing only in the signs of their roots. It is hoped that this factorization technique will provide a motivation to perform the factorization of two-variable positive function to generate scattering Hurwitz polynomials in two variables for which root finding methods are not applicable.
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