User menu

Factorization of a rational matrix : the singular case

Bibliographic reference Van Dooren, Paul. Factorization of a rational matrix : the singular case. In: Integral Equations and Operator Theory, Vol. 7, p. 704-741 (1984)
Permanent URL
  1. Anderson B.D.O., Moylan P.J., ?Spectral factorization of a finite-dimensional nonstationary matrix covariance?,IEEE Trans. Aut. Contr., Vol. AC-19, pp. 680?692, 1974.
  2. Anderson B.D.O., Moore J., ?Optimal Filtering?, Prentice-Hall, Englewood Cliffs, NJ, 1979.
  3. Bart H., Gohberg I., Kaashoek M., ?Minimal factorization of matrix and operator functions?, Birkhauser, Basel, 1979.
  4. Bart H., Gohberg I., Kaashoek M., Van Dooren P., ?Factorizations of transfer functions?,SIAM Contr. Vol. 18, pp. 675?696, 1980.
  5. Belevitch V., ?Classical Network Theory?, Holden Day, San Francisco, 1968.
  6. Cohen N., ?On minimal factorizations of rational matrix functions?,Int. Eq. & Op. Th., to appear.
  7. Dewilde P., Vandewalle J., ?On the factorization of a non-singular rational matrix?,IEEE Trans. Circ. & Syst., Vol. CAS-22, pp. 387?401, 1975.
  8. Emre E., ?Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces?,SIAM Contr., Vol. 18, pp. 288?296, 1980.
  9. Forney G., ?Minimal bases of rational vector spaces with applications to multivariable linear systems?,SIAM Contr., Vol. 13, pp. 493?520, 1975.
  10. Gantmacher F. ?Theory of Matrices I & II?, Chelsea, New York, 1959.
  11. Kailath T., ?Linear Systems?, Prentice Hall, Englewood Cliffs, NJ, 1980.
  12. Kalman R., ?Irreducible realization and the degree of a rational matrix?,SIAM Appl. Math., Vol. 13, pp. 520?544, 1965.
  13. Kublanovskaya V., ?AB algorithm and its modification for the spectral problem of linear pencils of matrices?, LOMI-preprint E-10-81, USSR Academy of Sciences, 1981.
  14. Kublanovskaya V., ?On an algorithm for the solution of spectral problems of linear matrix pencils?, LOMI-preprint E-1-82, USSR Academy of Sciences, 1982.
  15. Kwakernaak H., Sivan R., ?Linear Optimal Control Systems?, Wiley, New York, 1972.
  16. McMillan B., ?Introduction to formal realizability theory I & II?,Bell Syst. Tech. J., Vol. 31, pp. 217?279, pp. 541?600, 1952.
  17. Moler C., Stewart G., ?An algorithm for the generalized matrix eigenvalue problem?,SIAM Num. Anal., Vol. 10, pp. 241?256, 1973.
  18. Molinari B., ?Equivalence relations for the algebraic Riccati equation?,SIAM Contr., Vol. 11, pp. 272?285, 1973.
  19. Pernebo L., ?An algebraic theory for the design of controllers for linear multivariable systems. I & II,?IEEE Trans. Aut. Contr., Vol. AC-26, pp. 171?182, pp. 183?193, 1981.
  20. Rosenbrock H., ?State Space and Multivariable Theory?, Wiley & Sons, New York, 1970.
  21. Silverman L., ?Discrete Riccati equations: alternative algorithms, asymptotic properties and system theoretic interpretations?, inControl and Dynamic Systems, Vol. 12, pp. 313?385, Academic Press, New York, 1976.
  22. Stewart G., ?Error perturbation bounds for subspaces associated with certain eigenvalue problems?,SIAM Rev., Vol. 15, pp. 727?764, 1973.
  23. Stewart G., ?Algorithm 506: HQR3 and EXCHNG. Fortran subroutines for calculating and ordering the eigenvalues of a real upper Hessenberg matrix?,ACM TOMS, Vol. 2, pp. 275?280, 1976.
  24. Van Dooren P., ?The computation of Kronecker's canonical form of a singular pencil?,Lin. Alg. & Appl., Vol. 27, pp. 103?141, 1979.
  25. Van Dooren P., ?The generalized eigenstructure problem in linear system theory?,IEEE Trans. Aut. Contr., Vol. AC-26, pp. 111?129, 1981.
  26. Van Dooren P., ?A generalized eigenvalue approach for solving Riccati equations?,SIAM Sci. Stat. Comp., Vol. 2, pp. 121?135, 1981.
  27. Van Dooren P., ?A new numerical method for factorization and related problems in system theory?, in Proceedings Eur. Conf. Circ. Th. Design, The Hague, pp. 538?544, 1981.
  28. Van Dooren P., ?Reducing subspaces: computational aspects and applications in linear systems theory?, inLecture Notes on Control and Optimization, Vol. 44, pp. 935?953, Springer, New York, 1982.
  29. Van Dooren P., ?Reducing subspaces: definitions, properties and algorithms?, in Matrix Pencils, Eds. A. Ruhe & B. Kagstrom,Lecture Notes in Mathematics, Vol. 973, pp. 58?73, Springer, New York, 1983.
  30. Van Dooren P., Dewilde P., ?Minimal cascade factorization of real and complex rational transfer matrices?,IEEE Trans. Circ. & Syst., Vol. CAS-28, pp. 390?401, 1981.
  31. Van Dooren P., Dewilde P., ?Cascade factorization: a numerical approach?, Proceedings 4th Int. Symp. Math. Th. Netw. Syst., pp. 64?71, 1981.
  32. Van Dooren P., Dewilde P., ?The eigenstructure of an arbitrary polynomial matrix: computational aspects?,Lin. Alg. & Appl., Vol. 50, pp. 545?579, 1983.
  33. Verghese G., Van Dooren P., Kailath T., ?Properties of the system matrix of a generalized state-space system?,Int. J. Contr., Vol. 30, pp. 235?243, 1979.
  34. Wilkinson J., ?The Algebraic Eigenvalue Problem?, Oxford Univ. Press, London, 1965.
  35. Wilkinson J., ?Linear differential equations and Kronecker's canonical form?, inRecent Advances in Numerical Analysis?, Ed. C. de Boor, G. Golub, Academic Press, New York, 1978.
  36. Wolovich W. A., Linear Multivariable Systems, ISBN:9780387901015, 10.1007/978-1-4612-6392-0
  37. Wonham Walter Murray, Linear Multivariable Control, ISBN:9783662226759, 10.1007/978-3-662-22673-5
  38. Youla D., ?On the factorization of rational matrices?,IRE Trans. Inf. Theory, Vol. IT-7, pp. 172?189, 1961.