Computation of coprime factorizations of rational matrices

Linear Algebra and Its Applications

Volumn 271, Issue 1-3, 1998, Pages 83-115

  Varga, A ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042528119     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)00256-5     Document Type: Article

References (31)

1. V. Belevitch, Classical Network Theory, Holden Day, San Francisco, 1968.
2. A. Bunse-Gerstner, V. Mehrmann, and N. K. Nichols, Regularization of descriptor systems by derivative and proportional state feedback, SIAM J. Matrix Anal. Appl. 13:46-67 (1992).
3. T. Chan, Rank revealing QR factorizations, Linear Algebra Appl. 88/89:67-82 (1987).
4. F. R. Chang, C. H. Fang, and C. H. Wang, Doubly coprime matrix-fraction representations using proportional and derivative feedback concepts in generalized state-space systems, IEEE Trans. Automat. Control 36:1193-1195 (1991).
5. G. H. Golub and C. F. Van Loan, Matrix Computations, John Hopkins U.P., Baltimore, 1983.
6. ∞, Internat. J. Control 49:269-307 (1989).
7. H. Kwakernaak, State space algorithms for polynomial matrix computations, in Proceedings of the EURACO Workshop, Florence, Italy, 1995, pp. 133-170.
8. Y. Liu and B. D. O. Anderson, Controller reduction via stable factorization and balancing, Internat. J. Control 44:507-531 (1986).
9. P. Misra, P. Van Dooren, and A. Varga, Computation of structural invariants of generalized state-space systems, Automatica 30:1921-1936 (1994).
10. C. B. Moler and G. W. Stewart, An algorithm for generalized matrix eigenvalue problem, SIAM J. Numer. Anal. 10:241-256 (1973).
11. H. H. Rosenbrock, State-Space and Multivariable Theory, Wiley, New York, 1970.
12. ∞ control: A J-lossless coprime factorization approach, IEEE Trans. Automat. Control 38:1143-1147 (1993).
13. P. Van Dooren, The computation of Kronecker's canonical form of a singular pencil, Linear Algebra Appl. 27:103-141 (1979).
14. P. Van Dooren, Computing the eigenvalues of a polynomial matrix, in Proceedings of the IBM-NFWO Symposium, Brussels, 1979, pp. 213-223.
15. P. Van Dooren, A generalized eigenvalue approach for solving Riccati equations, SIAM J. Sci. Statist. Comput. 2:121-135 (1981).
16. P. Van Dooren, Rational and polynomial matrix factorizations via recursive pole-zero cancellation, Linear Algebra Appl. 137/138:663-697 (1990).
17. J. Vandewalle and P. Dewilde, On the irreducible cascade synthesis of a system with real rational transfer matrix, IEEE Trans. Circuits and Systems, 24:481-494 (1977).
18. A. Varga, A Schur method for pole assignment, IEEE Trans. Automat. Control 26:517-519 (1981).
19. A. Varga, The numerical stability of an algorithm for pole assignment, in Proceedings of the 2nd IFAC CADCS Symposium, West Lafayette, IN (G. Leininger, Ed.), Pergamon, Oxford, 1982, pp. 117-122.
20. A. Varga, A pole assignment algorithm for systems in generalized state-space form, in Proceedings of the 5th International Conference on Control and Informational Systems in Industry, Bucharest, Romania, 1983.
21. A. Varga, Computation of irreducible generalized state-space realizations, Kybernetika 26:89-106 (1989).
22. A. Varga, Coprime factors model reduction based on accuracy enhancing techniques, Systems Anal. Modelling and Simulation 11:303-311 (1993).
23. A. Varga, A Schur method for computing coprime factorizations with inner denominators and applications in model reduction, in Proceedings of the 1993 American Control Conference, San Francisco, 1993, pp. 2130-2131.
24. A. Varga, On computing inner-outer factorizations of rational matrices, in Proceedings of the 1995 European Control Conference, Rome, 1995, Vol. 3, pp. 2241-2246.
25. A. Varga, On stabilization of descriptor systems, Systems Control Lett. 24:133-138 (1995).
26. A. Varga, Computation of Normalized Coprime Factorizational of Rational Matrices, Systems Control Lett., to appear.
27. A. Varga and T. Katayama, Computation of J-inner-outer factorizations of rational matrices, Internat. J. Robust and Nonlinear Control, to appear.
28. G. Verghese, B. Lévy, and T. Kailath, A generalized state-space for singular systems, IEEE Trans. Automat. Control 26:811-831 (1981).
29. F. Y. Wang and M. J. Balas, Doubly coprime fractional representations of generalized dynamical systems, IEEE Trans. Automat. Control 34:733-744 (1989).
30. Z. Zhang and J. S. Freudenberg, Loop transfer recovery for non-minimum phase plants, IEEE Trans. Automat. Control 35:547-553 (1990).
31. Z. Zhang and J. S. Freudenberg, Formulas for minimum-phase/all-pass factorization of discrete-time transfer functions, Control Theory Adv. Tech. 8:743-754 (1992).