Orthonormal basis functions for modelling continuous-time systems

Signal Processing

Volumn 77, Issue 3, 1999, Pages 261-274

  Akçay, Hüseyin ^a   Ninness, Brett ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; FUNCTIONS; MATHEMATICAL MODELS; POLES AND ZEROS;

BASIS FUNCTIONS; CONTINUOUS TIME MODELS;

SIGNAL FILTERING AND PREDICTION;

EID: 0344210416     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1684(99)00039-0     Document Type: Article

References (44)

1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1965.
2. N. Achieser, Theory of Approximation, Dover, New York, 1992.
3. Akçay H., Ninness B. Rational basis functions for robust identification from frequency and time domain measurements. Automatica. 34:1998;1101-1117.
4. p convergence, Math. Control, Signals Systems (1999), to appear.
5. D.S. Bayard, Multivariable frequency domain identification via 2-norm minimization, Proceedings of the American Control Conference, Chicago, IL, 1992, pp. 1253-1257.
6. Bayard D.S. High-order multivariable transfer function curve fitting: Algorithms, sparse matrix methods and experimental results. Automatica. 30:1994;1439-1444.
7. P. Bodin, T. Oliveira e Silva, B. Wahlberg, On the construction of orthonormal basis functions for system identification, Proceedings of 13th IFAC World Congress, San Francisco, 1996, pp. 291-296.
8. 2 , Tech. Report, Computer and Automation Institute, Hungarian Academy of Sciences, 1995.
9. Cluett W., Wang L. Frequency smoothing using Laguerre model. in: Proc. IEE-D. 139:1992;88-96.
10. Davidson G., Falconer D. Reduced complexity echo cancellation using orthonormal functions. IEEE Trans. Circuits Systems. 38:1991;20-28.
11. den Brinker A.C. Laguerre-domain adaptive filters. IEEE Trans. Signal Process. 42:1994;953-956.
12. Dudley Ward N.F., Partington J.R. Robust identification in the disc algebra using rational wavelets and orthonormal basis functions. Internat. J. Control. 64:1996;409-423.
13. Dudley Ward N.F., Partington J.R. A construction of rational wavelets and frames in Hardy-Sobolev spaces with applications to system modelling. SIAM J. Control Optim. 36:1998;654-679.
14. B. Epstein, Orthogonal Families of Analytic Functions, Macmillan, New York, 1965.
15. J.B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
16. J. Golub, C. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1989.
17. Head J. Approximation to transient by means of Laguerre series. Proc. Cambridge Philos. Soc. 52:1956;640-651.
18. P. Heuberger, P.M.J. Van den Hof, O. Bosgra, A generalized orthonormal basis for linear dynamical systems, IEEE Trans. Automat. Control AC-40 (1995) 451-465.
19. W.H. Kautz, Network synthesis for specified transient response, Tech. Report 209, Massachusetts Institute of Technology, Research Laboratory of Electronics, 1952.
20. Kautz W.H. Transient synthesis in the time domain. IRE Trans. Circuit Theory. 1:1954;29-39.
21. Y. Lee, Synthesis of electric networks by means of the Fourier transforms of Laguerre's functions, J. Math. Phys. XI (1933) 83-113.
22. E.C. Levy, Complex curve fitting, IRE Trans. Automat. Control AC-4 (1959) 37-44.
23. Mäkila P. Approximation of stable systems by Laguerre filters. Automatica. 26:1990;333-345.
24. Mäkilä P. Laguerre series approximation of infinite dimensional systems. Automatica. 26:1990;985-995.
25. ∞ identification of continuous-time systems Internat. J. Control. 53:1991;689-707.
26. F. Malmquist, Sur la détermination d'une classe de fonctions analytiques par leurs valeurs dans un ensemble donné de points, in: Proceedings of Comptes Rendus du Sixième Congrès des mathématiciens scandinaves, Copenhagen, 1925, pp. 253-259.
27. T. McKelvey, H. Akçay, L. Ljung, Subspace-based multivariable system identification from frequency response data, IEEE Trans. Automat. Control AC-41 (1996) 960-979.
28. Mendel J. A unified approach to the synthesis of orthonormal exponential functions useful in systems analysis. IEEE Trans. Systems Sci. Cybernet. 2:1966;54-62.
29. S.O.R. Moheimani, H.R. Pota, I.R. Petersen, Spatial control for active vibration control of piezoelectric laminates, Proceedings of 37th IEEE Conference on Decision and Control, Tampa, Florida, 1998, pp. 4308-4313.
30. Nie X., Raghuramireddy D., Unbehauen R. Orthogonal expansion of stable rational transfer functions. Electron. Lett. 27:1991;1492-1494.
31. Ninness B., Gustafsson F. A unifying construction of orthonormal bases for system identification. IEEE Trans. Automat. Control. 42:1997;515-521.
32. Ü. Nurges, Laguerre models in problems of approximation and identification, in: Adaptive Systems, Plenum, 1987, pp. 346-352. Translated from Avtomatica i Telemekhanika 3 (March 1987) 88-96.
33. Partington J.R. Approximation of delay systems by Fourier-Laguerre series. Automatica. 27:1991;569-572.
34. Perez H., Tsujii S. A system identification algorithm using orthogonal functions. IEEE Trans. Signal Process. 38:1991;752-755.
35. Pintelon R., Guillaume P., Rolain Y., Schoukens J., Van Hamme H. Parametric identification of transfer functions in the frequency domain - a survey. IEEE Trans. Automat. Control. 39:1994;2245-2260.
36. Ross D. Orthonormal exponentials. IEEE Trans. Commun. Electron. 71:1964;173-176.
37. W. Rudin, Real and Complex Analysis, third ed., McGraw-Hill, New York, 1987.
38. C.K. Sanathanan, J. Koerner, Transfer function synthesis as a ratio of two complex polynomials, IEEE Trans. Automat. Control AC-8 (1963) 56-58.
39. M.D. Sidman, F.E. DeAngelis, G.C. Verghese, Parametric system identification on logarithmic frequency response data, IEEE Trans. Automat. Control AC-36 (1991) 1065-1070.
40. S. Takenaka, On the orthogonal functions and a new formula of interpolation, Jpn. J. Math. II (1925) 129-145.
41. B. Wahlberg, System identification using Laguerre models, IEEE Trans. Automat. Control AC-36 (1991) 551-562.
42. B. Wahlberg, System identification using Kautz models, IEEE Trans. Automat. Control AC-39 (1994) 1276-1282.
43. Wahlberg B., Mäkilä P. On approximation of stable linear dynamical systems using Laguerre and Kautz functions. Automatica. 32:1996;693-708.
44. Zervos C., Belanger P., Dumont G. Controller tuning using orthonormal series identification. Automatica. 24:1988;165-175.