On Polynomial Matrix Spectral Factorization by Symmetric Extraction

IEEE Transactions on Automatic Control

Volumn 30, Issue 5, 1985, Pages 453-464

  Callier, Frank M ^a  

^a UNIVERSITY OF NAMUR   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - POLYNOMIALS;

DIAGONAL REDUCEDNESS; POLYNOMIAL MATRICES; POLYNOMIAL MATRIX SPECTRAL FACTORIZATION; SYMMETRIC EXTRACTION;

COMPUTER PROGRAMMING;

EID: 0022060394     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1985.1103973     Document Type: Article

References (31)

1. D. C. Youla, “On the factorization of rational matrices,'' IRE Trans. Inform. Theory, vol. IT-7, pp. 172–179, 1961.
2. M. C. Davis, “Factoring the spectral matrix,” IEEE Trans. Auto-mat. Contr., vol. AC-8, pp. 296–305, 1963.
3. M. G. Strintziss, “A solution to the matrix factorization problem,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 225–232, 1972.
4. J. P. Vandewalle and P. Dewilde, “On the minimal spectral factorization of nonsingular positive rational matrices,” IEEE Trans. Inform. Theory, vol. IT-21, pp. 612–618, 1975.
5. B. D. O. Anderson, “An algebraic solution to the spectral factorization problem,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 410–414, 1967.
6. B. D. O. Anderson, K. L. Hitz, and N. D. Diem, “Recursive algorithm for spectral factorization,” IEEE Trans. Circuits Syst., vol. CAS-21, pp. 742–750, 1974.
7. G. T. Wilson, “The factorization of matricial spectral densities,” SIAM J. Appl. Math., vol. 23, pp. 420–426, 1972.
8. G. T. Wilson, “A convergence theorem for spectral factorization,” J. Multivariate Anal., vol. 8, pp. 222–232, 1978.
9. Z. Vostry, “New algorithm for polynomial spectral factorization with quadratic convergence: Part I,” Kybernetica (Prague), vol. 11, pp. 415–422, 1975; “New algorithm for polynomial spectral factorization with quadratic convergence: Part II,” Kybernetica (Prague), vol. 12, pp. 248–259, 1976.
10. J. Rissanen, “Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with applications to factoring positive matrix polynomials,” Math. Comput., vol. 27, pp. 147–155, 1973.
11. D. C. Youla and N. N. Kazanjian, “Bauer-type factorization of positive matrices and the theory of matrix polynomials orthogonal on the unit circle,” IEEE Trans. Circuits Syst., vol. CAS-25, pp. 57–69, 1978.
12. P. Delsarte, Y. Genin, and Y. Kamp, “A simple approach to spectral factorization,” IEEE Trans. Circuits Syst., vol. CAS-25, pp. 943–946, 1978.
13. V. Kucera, “New results in state estimation and regulation,” Automatica, vol. 17, pp. 745–748, 1981.
14. F. M. Callier, “Partially stable LQ-optimal control by spectral factorization,” Int. J. Contr., vol. 39, no. 3, pp. 523–539, 1984.
15. A. C. Pugh and P. A. Rathcliffe, “On the zeros and poles of a rational matrix,” Int. J. Contr., vol. 30, pp. 213–226, 1979.
16. J. P. Vandewalle and P. Dewilde, “On the irreducible cascade synthesis of a system with a real rational transfer matrix,” IEEE Trans. Circuits Syst., vol. CAS-24, pp. 481–494 (esp. p. 483, definitions, 1st column), 1977.
17. F. M. Callier, and C. A. Desoer, Multivariable Feedback Systems. New York: Springer-Verlag, 1982, pp. 67–71, 80–83, and 116.
18. W. A. Wolovich, Linear Multivariable Systems. New York: Springer-Verlag, 1974.
19. S. H. Wang, “Design of linear multivariable systems,” Electron. Res. Lab., Univ. Calif., Berkeley, Memo. ERL-M309, pp. 11–14, Oct. 1971.
20. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
21. V. Belevitch, Classical Network Theory. San Francisco, CA: Holden Day, 1968; pp. 362–363.
22. Y. Oono and K. Yasuura, “Synthesis of finite passive 2n-terminal networks with prescribed scattering matrices,” in Memoirs of the Faculty of Engineering, Kyushu Univ., vol. XIV, no. 2, May 1954 (reprinted Fukuoka, Japan, 1963), pp. 125–177 (esp. pp. 169–170).
23. I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials. New York: Academic, 1980.
24. F. R. Gantmacher, The Theory of Matrices, vol. I. New York: Chelsea, 1959, pp. 19–22.
25. G. Strang, Linear Algebra and its Applications. New York: Academic, 2nd ed., 1980.
26. A. Ruhe, “Algorithms for the nonlinear eigenvalue problem,” SIAM J. Numer. Anal., vol. 10, pp. 674–689, 1973.
27. J. H. Wilkinson, Rounding Errors in Algebraic Processes. Englewood Cliffs, NJ: Prentice-Hall, 1963.
28. J. Jezek, and V. Kucera, “Efficient algorithm for spectral factorization,” in Proc. 9th IFAC World Congress, Budapest, Hungary, 1984; Automatica. to be published.
29. A. Laub, “A Schur method for solving algebraic Riccati equations,” IEEE Trans. Automat. Contr., vol. AC-24, pp. 913–921, 1979.
30. P. Van Dooren, “A generalized eigenvalue approach for solving Riccati equations,” SIAM J. Sci. Stat. Comp., vol. 2, pp. 121–135, 1981.
31. N. K. Jain and K. Singhal, “On Kublanovskaya's approach to the solution of the generalized latent value problem for functional λ-matrices.” SIAM J. Numer. Anal., vol. 20, pp. 1062–1070, 1983.