Stable Factorization of Strictly Hurwitz Polynomials
Keywords:
Routh-Hurwitz stability, Hurwitz polynomial, stable factorization, Newton’s methodAbstract
We 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.References
Aksen A., "Design of Lossless Two-ports with Mixed, Lumped and Distributed Elements for Broadband Matching," PhD. Dissert., Lehrstuhl Für Nachrichtentechnik, Ruhr Universitaet Bochum, 1994.
Fettweis A., "On the Scattering Matrix and the Transfer Scattering Matrix of Multi Dimensional Lossless Two-ports," Int. J. of Communication, vol. 36, pp. 374-381.
Henrici P., Applied and Computational Complex Analysis, Vol. II, Wiley, New York, 1977.
Lang S., Linear Algebra, Addison-Wesley, Reading, MA, 1966, p. 183.
Yarman B. S., "Broadband Networks," Wiley Encyclopedia of Electrical and Electronics Engineering, Vol. II, pp. 589-604, 1999. http://dx.doi.org/10.1002/047134608x.w2511
Yarman B. S. and Aksen A., "A Reflectance-based Computer Aided Modeling Tool for High Speed/High Frequency Communication Systems," Proc. IEEE-ISCAS 2001; 4, pp. 270-273.
Yarman B. S., Aksen A. and Kilinc A., "Immitance Data Modeling via Linear Interpolation Techniques," Proc. IEEE-ISCAS 2002; 3, pp. 527-530.
Yarman B. S., Kilinc A. and Aksen A., "Immitance Data Modeling via Linear Interpolation Techniques: a Classical Circuit Theory Approach," Int. J. of Circuit Theory and Applications, 2004; 32, pp. 537-563. http://dx.doi.org/10.1002/cta.295
Yarman B. S. and Carlin H. J., "A Simplified Real Frequency Technique Applied to Broadband Multi-stage Amplifiers," IEEE Trans. MTT; 30, pp. 2216-2222, 1982. http://dx.doi.org/10.1109/TMTT.1982.1131411
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