Balanced parametrizations of stable SISO all-pass systems in discrete time

Mathematics of Control, Signals, and Systems

Volumn 13, Issue 3, 2000, Pages 240-276

  Hanzon, Bernard ^a   Peeters, Ralf L M ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; TOPOLOGY;

BALANCED REALIZATION; SCHUR PARAMETERS; SINGLE-OUTPUT SINGLE-INPUT SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 0033676534     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009869     Document Type: Article

References (45)

1. B. D. O. Anderson, E. I. Jury, and M. Mansour, Schwarz matrix properties for continuous and discrete time systems, Intentat. J. Control 23, 1-16, 1976.
2. B. D. O. Anderson, E. I. Jury, and M. Mansour, On model reduction of discrete time systems, Automatica 22, 717-721, 1986.
3. L. Baratchart, On the topological structure of inner functions and its use in identification of linear systems, in: B. Bonnard, B. Bride, J. P. Gauthier, and I. Kupka (eds.), Analysis of Controlled Dynamical Systems, pp. 51-59. Boston: Birkhäuser, 1991.
4. E. Badreddin and M. Mansour, Model reduction of discrete time systems using Schwarz canonical form. Electron. Lett. 16, 782-783, 1980.
5. R. W. Brockett, Some geometric questions in the theory of linear systems, IEEE Trans. Automat. Control 21, 449-455, 1976.
6. B. Friedland, Control System Design. New York: McGraw-Hill, 1986.
7. P. A. Fuhrmann, A Polynomial Approach to Linear Algebra. Berlin: Springer-Verlag, 1996.
8. P. A. Fuhrmann and U. Helmke, On complex parameterizations of real rational functions, Arch. Elektron. Übertragungstechnik 49(5/6), 293-306, 1995.
9. F. R. Gantmacher, The Theory of Matrices. Vols. I and II. New York: Chelsea, 1959.
10. Y. Genin, P. Van Dooren, T. Kailath, J.-M. Delosme, and M. Morf, On Σ-lossless transfer functions and related questions, Linear Algebra Appl. 50, 251-275. 1983.
11. P. E. Gill and W. Murray, Modification of matrix factorizations after a rank-one change, in: D. Jacobs (ed.), The State of the Art in Numerical Analysis, pp. 55-83. New York: Academic Press, 1977.
12. x-error bounds, Internat. J. Control 39(6), 1115-1193, 1984.
13. G. H. Golub and C. F. van Loan, Matrix Computations, 2nd edn. Baltimore, MD: Johns Hopkins University Press, 1989.
14. W. B. Gragg, Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle (in Russian), pp. 16-32, in: E. S. Nikolaev (ed), Numerical Methods in Linear Algebra. Moscow: Moscow U.P., 1982; English transl., rev., J. Comput. Appl. Math. 46, 183-198, 1993.
15. W. B. Gragg, Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle (in Russian), pp. 16-32, in: E. S. Nikolaev (ed), Numerical Methods in Linear Algebra. Moscow: Moscow U.P., 1982; English transl., rev., J. Comput. Appl. Math. 46, 183-198, 1993.
16. B. Hanzon, Identifiability, Recursive Identification, and Spaces of Linear Dynamical Systems. CWI Tracts 63, 64. Amsterdam: Centre for Mathematics and Computer Science, 1989.
17. B. Hanzon, On the differentiable manifold of fixed order stable linear systems, Systems Control Lett. 13, 345-352, 1989.
18. B. Hanzon, A new balanced canonical form for stable multivariable systems, IEEE Trans. Automat. Control 40, 374-378, 1995.
19. B. Hanzon and J. M. Maciejowski, Constructive algebra methods for the L2 problem for stable linear systems. Automatica 32(12), 1645-1657, 1996.
20. B. Hanzon and R. J. Ober, Overlapping block-balanced canonical forms and parametrizations: the stable SISO case, SIAM J. Control Optim. 35(1), 228-242, 1997.
21. B. Hanzon and R. J. Ober, Overlapping block-balanced canonical forms for various classes of linear systems, Linear Algebra Appl. 281, 171-225, 1998.
22. B. Hanzon and R. L. M. Peeters, A Faddeev sequence method for solving Lyapunov and Sylvester equations, Linear Algebra Appl. 241-243, 401-430, 1996.
23. B. Hanzon and R. L. M. Peeters, Balanced Parametrizations of Stable SISO All-Pass Systems in Discrete-Time. Report M 97-05. Dept. Mathematics, Maastricht University, Maastricht, 1997.
24. U. Helmke, A global parametrization of asymptotically stable linear systems, Systems Control Lett. 13, 383-389, 1989.
25. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
26. T. Kailath and A. H. Sayed, Displacement structure: theory and applications, SIAM Rev. 37(3), 297-386, 1995.
27. R. E. Kalman, P. L. Farb, and M. A. Arbib, Topics in Mathematical Systems Theory. New York: McGraw-Hill, 1969.
28. H. Kimura, Generalized Schwarz form and lattice-ladder realizations of digital filters, IEEE Trans. Circuits and Systems 32(11), 1130-1139, 1985.
29. H. Kimura, Positive partial realization of covariance sequences, in: C. I. Byrnes and A. Lindquist (eds.), Modelling, Identification and Robust Control, pp. 499-513. Amsterdam: North-Holland, 1986.
30. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd edn. New York: Academic Press, 1985.
31. H. J. Landau, Maximum entropy and the moment problem. Bull. Amer. Math. Soc. 16, 47-77, 1987.
32. B. C. Moore, Principal component analysis in linear systems: controllability, observability and model reduction, IEEE Trans. Automat. Control 26, 17-32, 1981.
33. C. T. Mullis and R. A. Roberts, Synthesis of minimum roundoff noise fixed point digital filters, IEEE Trans. Circuits and Systems 23, 551-562, 1976.
34. R. J. Ober, Balanced realizations: canonical form, parametrization, model reduction, Internat. J. Control 46, 643-670, 1987.
35. R. J. Ober, Connectivity properties of classes of linear systems, Internal. J. Control 50, 2049-2073, 1989.
36. R. Ober, Balanced parametrization of classes of linear systems, SIAM J. Control Optim. 29, 1251-1287, 1991.
37. R. L. M. Peeters and B. Hanzon, A balanced canonical form for discrete-time stable all-pass systems, in: U. Helmke, R. Mennicken, and J. Saurer (eds.), Systems and Networks: Mathematical Theory and Applications, Vol. II, pp. 417-420. Berlin: Akademie Verlag, 1994.
38. L. Pernebo and L. M. Silverman, Model Reduction via Balanced State Space Representations, IEEE Trans. Automat. Control 27, 382-387, 1982.
39. A. L. Rijkebocr, Fisher optimal approximation of an AR(n)-process by an AR(n - 1)-process, in: J. W. Nieuwenhuis, C. Praagman, and H. L. Trentelman (eds.), Proceedings of the 2nd European Control Conference ECC '93, 1225-1229, Groningen, 1993.
40. A. L. Rijkeboer, Differential Geometric Models for Time-Varying Coefficients of Autoregressive Processes. Doctoral dissertation, Katholieke Universiteit Brabant, Tilburg, 1994.
41. W. Rudin, Real and Complex Analysis, 2nd edn. New Delhi: Tata McGraw-Hill, 1974.
42. G. Segal, The topology of spaces of rational functions, Acta Math. 143, 39-72, 1979.
43. T. Söderström and P. Stoica, System Identification. New York: Prentice-Hall, 1989.
44. M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: The MIT Press, 1985.
45. N. Young, An Introduction to Hilbert Space. Cambridge: Cambridge University Press, 1988.