Minimal Cascade Factorization of Real and Complex Rational Transfer Matrices

IEEE Transactions on Circuits and Systems

Volumn 28, Issue 5, 1981, Pages 390-400

  Dewilde, Patrick ^b  

^a Phillips Research Laboratory ^*  (United States)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES;

EID: 0019571936     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1981.1085000     Document Type: Article

References (32)

1. B. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis. A Modern Systems Approach. NJ: Prentice Hall, 1972
2. H. Bart, I. Gohberg, and M. Kaashoek, “Minimal factorization of matrix and operator functions,” Birkhauser, Basel, 1979
3. H. Bart, I. Gohberg, M. Kaashoek, and P. Van Dooren, “Factorizations of transfer functions,” SIAM J. Contr. Opt., vol. 18, pp. 675–696, Nov. 1980
4. V. Belevitch, Classical Network Theory. San Francisco, CA: Holden Day, 1968
5. A. Bjorck and G. Golub, “Numerical methods for computing angles between linear subspaces,” Math. Comp., vol. 27, pp. 579–594, July 1973
6. M. Brodskii, “Unitary operator colligations and their characteristic functions,” Russ. Math. Surv., vol. 33, pp. 159– 191, 1978
7. C. Chen, Introduction to Linear System Theory. New York: Bolt Rinehart & Winston, 1970
8. P. Dewilde, “Minimal multivariable cascade synthesis: a structure theory,” in Proc. 20th Midwest Symp. Circuits Syst., Western Periodicals, pp. 782– 784, Aug. 1977
9. P. Dewilde, V. Belevitch, and R. Newcomb, “On the problem of degree reduction of a scattering matrix by factorization.” J. Franklin Inst., vol. 291, pp. 387–401, May 1971
10. P. Dewilde and J. Vandewalle, “On the factorization of a nonsingular rational matrix,” IEEE Trans. Circuits Syst., vol. CAS-22, pp. 637–645, 1975
11. M. Livsic, “Operators, oscillations, waves (open systems),” Amer. Math. Soc., 1972
12. B. McMillan, “Introduction to formal realizability theory I & II,” Bell Syst. Tech. J.,. vol. 31, pp. 217–279, pp. 541–600, 1952
13. B. Molinari, “Equivalence relations for the algebraic Riccati equation,” SIAM J. Contr., vol. 11, pp. 272–285, May 1973
14. B. Moore, “Singular value analysis of linear systems,” in Proc. 17th IEEE Conf. Dec. Contr., 66– 73, Jan. 1979
15. V. Potapov, “The multiplicative structure of J-contractive matrix functions,” Amer. Math. Soc. Transl., Ser. 2, vol. 15, pp. 131–244, 1960
16. H. Rosenbrock, State-space and Multivariable Theory. New York: Wiley, 1970
17. L. Sachnovic, “On the factorization of an operator-valued transfer function,” Sov. Math. Dokl., vol. 226, pp. 203–207, 1976
18. B. Smith et al., Matrix Eigensystem Routines. EISPACK Guide. New York: Springer, 1976
19. G. Stewart, Introduction to Matrix Computation. New York: Academic, 1973
20. ―,“Error and perturbation bounds for subspaces associated with certain eigenvalue problems,” SIAM Rev., vol. 15, pp. 727–764, Oct. 1973
21. ―, “Algorithm 506: HQR3 and EXCHNG. Fortran subroutines for calculating and ordering the eigenvalues of a real upper Hessenberg senberg matrix,” ACM TOMS, vol. 2, pp. 275–280, Sept. 1976
22. A. van der Sluis, “Condition numbers and equilibration of matrices,” Num. Math., vol. 14, pp. 14–23, Dec. 1969
23. J. 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, Sept. 1977
24. ―, “Local I/O structure theory for multivariable systems and applications to cascade realization, IEEE Circuits Syst., vol. CAS-25, 25, pp. 279–289, May 1978
25. P. Van Dooren, “The generalized eigenstructure problem. Applica tions in linear system theory,” Ph. D. dissertation, Kath. Univ. Leuven, Louvain, Belgium, May 1979
26. P. Van Dooren and P. Dewilde, “Minimal factorization of rational matrices,” in Proc. 17th IEEE Conf. Dec. Contr., pp. 170– 172, Jan. 1979
27. P. Van Dooren, P. Dewilde, and J. Vandewalle, “On the determination of the Smith-McMillan form of a rational matrix from its Laurent expansion,” IEEE Circuits Syst., vol. CAS-26, pp. 180– 189, Mar. 1979. Í‘
28. J. Wilkinson, The Algebraic Eigenvalue Problem. Oxford: Clarendon, 1965
29. J. Wilkinson and C. Reinsch, “Handbook for automatic computations II: Linear algebra,” Berlin: Springer, 1971
30. J. Willems, “Least squares stationary optimal control and the algebraic Riccati equation,” IEEE Trans. Automat. Contr., vol. AC-16, 621–634, Dec. 1971
31. D. Youla and P. Tissi, “N-port synthesis via reactance extraction. Part I,” in 1966 IEEE Int. Conv. Rec., pp. 183–208, 1966
32. P. Van Dooren, “The generalized eigenstructure problem in linear system theory,” IEEE Trans. Automat. Contr., vol. AC-26, Feb. 1981