On approximation of stable linear dynamical systems using Laguerre and Kautz functions

Automatica

Volumn 32, Issue 5, 1996, Pages 693-708

  Wahlberg, B ^a   Makila P M ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Laguerre functions; Linear systems; Model approximation; Model reduction; Orthonormal basis functions

Indexed keywords

CONTROL SYSTEM ANALYSIS; DESCRIBING FUNCTIONS; MATHEMATICAL MODELS; SYSTEM STABILITY;

KAUTZ FUNCTIONS; LAGUERRE FUNCTIONS; STABLE LINEAR DYNAMICAL SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 0030143276     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(95)00198-0     Document Type: Article

References (68)

1. Ahlfors, L. V. (1979). Complex Analysis, Third Edn. McGraw-Hill, New York.
2. Beckmann, P. (1973). Orthogonal Polynomials for Engineers and Physicists. The Golden Press.
3. Bodin, P. and Wahlberg, B. (1994). Thresholding in high order transfer function estimation. In Proc. 33th CDC, pp. 3400-3405, Orlando, FL.
4. Broome, P. W. (1965). Discrete orthonormal sequences. J. of the Association for Computing Machinary, 12(2), 151-168.
5. Chihara, T. S. (1978). An Introduction to Orthogonal Polynomials. Mathematics and its Applications, Vol. 13. Gordon and Breach, Reading, U.K.
6. Clement, P. R. (1982). Laguerre functions in signal analysis and parameter identification. J. Franklin Inst., 313(2), 85-95.
7. Clement, P. R. (1985). Application of generalized Laguerre functions. Mathematics and Computers in Simulation, 27, 541-550.
8. Clowes, G. J. (1965). Choice of the time-scaling factor for linear system approximations using orthonormal Laguerre functions. IEEE Trans. Automat. Control, AC-10, 487-489.
9. Cluett, W. R. and Wang, L. (1992). Frequency smoothing using Laguerre model. IEE Proceedings-D, 139(1), 88-96.
10. den Brinker, A. C. (1993). Adaptive orthonormal filters. In Preprints 12th IFAC World Congress, Vol. 5, pp. 287-290, Sydney, Australia.
11. Dumont, G. A., Zervos, C. and Pageau, G. (1990). Laguerre-based adaptive control of PH in an industrial bleach plant extraction stage. Automatica, 26, 781-787.
12. Dumont, G. A. and Zervos, C. C. (1986). Adaptive controllers based on orthonormal series representations. In 2nd IFAC Workshop on Adaptive System in Control and Signal Processing, pp. 371-376, Lund, Sweden.
13. Finn, C., Ydstie, E. and Wahlberg, B. (1993). Contrained predictive control using orthogonal expansions. AIChE J., 39, 1810-1826.
14. Fu, Y. and Dumont, G. A. (1993a). An optimal time scale for discrete Laguerre network. IEEE Trans. Automat. Control, AC-38(6), 934-938.
15. Fu, Y. and Dumont, G. A. (1993b). On determination of Laguerre filter pole through step or impulse data. In Preprints 12th IFAC World Congress, Vol. 5, pp. 303-306, Sydney, Australia.
16. Glader, C., Högnäs, G., Mäkilä, P. M. and Toivonen, H. (1991). Approximation of delay systems - a case study. Int. J. Control, 53, 369-390.
17. ∞ approximants. Math. Control Sig. Sys., 4, 233-246.
18. Goodwin, G. C., Gevers, M. and Ninness, B. (1992). Quantifying the error in estimated transfer function with application to model order selection. IEEE Trans. Automat. Control, AC-37(7), 913-928.
19. Gottlieb, M. J. (1938). Polynomials orthogonal on finite or enumerable set of points. Amer. J. Mathematics, 60, 453-458.
20. Gu, G., Khargonekar, P. P. and Lee., E. B. (1989). Approximation of infinite-dimensional systems. IEEE Trans. Automat. Control, AC-34, 610-618.
21. Gunnarsson, S. and Wahlberg, B. (1991). Some Asymptotic Results in Recursive Identification using Laguerre Models. Int. J. of Adaptive Control and Signal Processing, 5, 313-333.
22. Head, J. W. (1956). Approximation to transient by means of Laguerre Series. Proc. Cambridge Phil. Soc., 52, 64-651.
23. Henrici, P. (1979). Fast Fourier methods in computational complex analysis. SIAM Rev., 21, 481-527.
24. Heuberger, P. (1991). On Approximate System Identification with System Based Orthonormal Functions. PhD thesis, Delft University of Technology, Delft, The Netherlands.
25. Heuberger, P., Van den Hof, P. and Bosgra, O. (1993). Modelling linear dynamical systems through generalized orthonormal basis functions. In Preprints 12th IFAC World Congress, Vol. 5, pp. 283-286, Sydney, Australia.
26. Horowitz, I. M. (1963). Synthesis of Feedback Systems. Academic Press, New York.
27. Huggins, W. H. (1956). Signal theory. IRE Trans. on Circuit Theory, CT-3(3), 210-216.
28. Kammler, D. W. and McGlinn, R. J. (1978). A bibliography for approximation with exponential sums. J. Comput. Appl. Math., 4(2), 167-173.
29. Kautz, W. H. (1952). Network synthesis for specified transient response. Technical report, 209, M.I.T. Research Lab., Electronics, Cambridge, MA.
30. Kautz, W. H. (1954). Transient synthesis in time domain. IRE Transactions on Circuit Theory, CT-1(3), 29-39.
31. King, R. E. and Paraskevopoulos, P. N. (1979). Parametric identification of discrete-time SISO systems. Int. J. Control, 30, 1023-1029.
32. Lai, D. C. (1985). Signal processing with orthonormalized exponentials. Mathematics and Computers in Simulation, 27, 409-420.
33. Lampard, D. G. and Levan, N. (1992). A new construction of multiple Laguerre shifts. Technical report, Electrical Engineering, University of California, Los Angeles, CA.
34. Lee, Y. W. (1931). Synthesis of electrical networks by means of Fourier transforms of Laguerre's functions. J. Math. Phy., 11, 83-113.
35. Lee, Y. W. (1961). Statistical Theory of Communications. J. Wiley & Sons, New York.
36. Lindskog, P. and Wahlberg, B. (1993). Application of Kautz models in system identification. In Preprints 12th IFAC World Congress, Vol. 5, pp. 308-312, Sydney, Australia.
37. Lorentz, G. G. (1986). Approximation of Functions. Chelsea, New York.
38. Mäkilä, P. M. (1990a). Approximation of stable systems by Laguerre filters. Automatica, 26(2), 333-345.
39. Mäkilä, P. M. (1990b). Laguerre series approximation of infinite dimensional systems. Automatica, 26(6), 985-996.
40. ∞ identification of continuos-time systems. Int. J. Control, 53, 689-707.
41. ∞. International Journal of Control, 58(3), 665-683.
42. Masani, P. R. (1990). Norbert Wiener. Vita Mathematica, Vol. 5, Birkhäuser, Basel, Boston, Berin.
43. Van den Hof, P., Heuberger, P. and Bokor, J. (1994). Identification with generalized orthonormal basis functions -statistical analysis and error bounds. In SYSID'94, Vol. 3, pp. 207-212, Copenhagen, Denmark.
44. Mendel, J. M. (1966). A unified approach to the synthesis of orthonormal exponential functions useful in systems analysis. IEEE Trans. Systems Science and Cybernetics, 2, 54-62.
45. Neuman, J. V. (1929). Zur theorie der unbeschrakten matrizen. J. fur Math., 161, 208-236.
46. Nurges, Y. (1987). Laguerre models in problems of approximation and identification of discrete systems. Automat. and Remote Control, 48, 346-352.
47. Nurges, Y. and Yaaksoo, Y. (1981). Laguerre state equations for multivariable discrete systems. Automat. and Remote Control, 42, 1601-1603.
48. Partington, J. R. (1991). Approximation of delay systems by Fourier-Laguerre series. Automatica, 27, 569-572.
49. Pati, Y. C. (1992). Wavelets and time-frequency methods in linear systems and neural networks. PhD thesis, University of Maryland, College Park, MD.
50. Pati, Y. C. and Khrishnaprasad, P. S. (1992). Rational waveelets in approximation and identification of stable linear systems. In Proc. 31th CDC, pp. 1502-1507, New York.
51. Pinkus, A. (1985). n-Widths in Approximation Theory. Springer, Berlin.
52. Rosenblum, M. and Rovnyak, J. (1985). Hardy Classes and Operator Theory. Oxford University Press, New York.
53. Ross, D. C. (1964). Orthonormal exponentials. IEEE Trans. Comm. Electronics, CE-12, 173-176.
54. Schetzen, M. (1970). Power-series equivalence of some functional series with applications. IEEE Trans. on Circuit Theory, CT-17(3), 305-313.
55. Söderström, T. and Stoica, P. G. (1989). System Identification. Prentice-Hall, Hemel Hempstead, U.K.
56. Steiglitz, K. (1965). Rational transform approximation via the Laguerre spectrum. J. Franklin Inst., 280, 387-394.
57. Szegö, G. (1939). Orthogonal Polynomials, American Mathematical Society Colloqium Publication Vol. XXII. American Mathematical Society, Rhode Island, NY.
58. Tricomi, F. (1935). Trasformazione di Laplace e polinomi di Laguerre. I.R.C. Accad. Lincei, 21, 235.
59. Wahlberg, B. (1991). System identification using Laguerre models. IEEE Trans. Automat. Control, AC-36(5), 551-562.
60. Wahlberg, B. (1994). System identification using Kautz models. IEEE Trans. Automat. Control, AC-39(6), 1276-1281.
61. Wahlberg, B. and Hannan, E. J. (1993). Parametric signal modelling using Laguerre filters. Annals of Applied Probability, 3(2), 467-496.
62. Wahlberg, B. and Lindskog, P. (1991). Approximate modelling by means of orthonormal functions. In Progress in Systems and Control Theory, G. De Masi, A. Gombani and A. Kurzhanski (eds). Birkhäuser, Basel, Boston and Berlin.
63. Wahlberg, B. and Ljung, L. (1992). Hard frequency domain model error bounds from least-squares like identification techniques. IEEE Trans. Automat. Control, AC-37(7), 900-912.
64. Wiener, N. (1956). The Theory of Prediction, Modern Mathematics for Engineers. Bechenbach, McGraw-Hill, New York.
65. Young, T. Y. and Huggins, W. H. (1962a). Complementary signals and orthogonalized exponentials. IRE Transactions on Circuit Theory, CT-9, 362-370.
66. Young, T. Y. and Huggins, W. H. (1962b). Discrete orthonormal exponentials. In Proc. Nat. Elec. Conf., pp. 10-18.
67. Zervos, C., Belanger, P. R. and Dumont, G. A. (1988). Controller tuning using orthonormal series identification. Automatica, 24, 165-175.
68. Zervos, C. and Dumont, G. A. (1988). Deterministic adaptive control based on Laguerre series representation. Int. J. Control, 48, 2333-2359.