Laguerre and Kautz shift approximations of delay systems

International Journal of Control

Volumn 72, Issue 10, 1999, Pages 932-946

  Makila P M ^a   Partington, J R ^b  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONTROL SYSTEM ANALYSIS; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS;

LAGUERRE-KAUTZ SHIFT APPROXIMATION;

DELAY CONTROL SYSTEMS;

EID: 0345102509     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/002071799220678     Document Type: Article

References (47)

1. Adamjan, V. M., Arov, D. Z., and Krein, M. G., 1971, Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem. Math. USSR Sbornik, 15, 31-73.
2. Astrom, K. J., and Hagglund, T., 1995, PID Controllers: Theory, Design, and Tuning. 2nd edn. (Research Triangle Park, USA: Instrument Society of America).
3. Bercovici, H., 1988. Operator theory and arithmetic in H (Providence, Rhode Island: American Mathematical Society).
4. Bonnet, C., and Partington, J. R., 1996, Bezout factors and L -optimal controllers for delay systems using a two-parameter compensator scheme. IEEE Transactions on Automatic Control (to appear).
5. Brethe, D., and Loiseau, J. J., 1997, Stabilization of time-delay systems. JESA-APII-RAIRO, 31, 1025-1042.
6. Coughanowr, D. R., and Koppel, L. B., 1965, Process Systems Analysis and Control (New York: McGraw-Hill).
7. Dudley Ward, N. F., and Partington, J. R., 1995, Rational wavelet decompositions of transfer functions in Hardy-Sobolev classes. Mathematics of Control, Signals and Systems, 8, 257-278.
8. Dudley Ward, N. F., and Partington, J. R., 1996, Robust identification in the disc algebra using rational wavelets and orthonormal basis functions. International Journal of Control, 64, 409-423.
9. Glader, C., Hognas, G., Makila, P. M., and Toivonen, H. 1991, Approximation of delay systems-a case study. International Journal of Control, 53, 369-390.
10. Glover, K., Curtain, R. F., and Partington, J. R., 1988, Realisation and approximation of linear in nite-dimen-sional systems with error bounds. SIAM Journal of Control Optimization, 26, 863-898.
11. Glover, K., Lam, J., and Partington, J. R., 1990, Rational approximation of a class of infinite-dimensional systems I: Singular values of Hankel operators. Mathematical Control of Signals and Systems, 3, 325-344.
12. x approximants. Mathematical Control of Signals and Systems, 4, 233-246.
13. Glover, K., Lam, J., and Partington, J. R., 1991b, Rational approximation of a class of infinite dimensional systems: The L2 case. In Progress in Approximation Theory, pp. 405-440 (New York: Academic Press) (Additional volume of Journal of Approximation Theory).
14. Heuberger, P., Van den Hof, P. M. J., and Bosgra, O. 1995, A generalized orthonormal basis for linear dynamical systems. IEEE Transactions on Automatic Control, 40, 451-465.
15. Horowitz, I. M., 1963, Synthesis of Feedback Systems (New York: Academic Press).
16. p 0, to). Journal of Approximation Theory, 16, 384-408.
17. Kautz, W. H., 1954, Transient synthesis in the time domain. IRE Transactions on Circuit Theory, CT(1), 29-39.
18. Kuo, F. F., 1966, Network Analysis and Synthesis, 2nd edn (New York: John Wiley &Sons).
19. Lam, J., 1994, Analysis on the Laguerre formula for approximating delay systems. IEEE Transactions on Automatic Control, 39, 1517-1521.
20. Levan, N., and Nambu, T., 1996, On a class of shifts and shift semigroups of finite multiplicities. Japan Journal of Industrial and Applied Mathematics, 13, 93-105.
21. MA'izi, N., 1993, A relaxation approach for the Hankel approximation of some vibrating structures. In R. F. Curtain, A. Bensoussan and J. L. Lions (Eds), Analysis and optimization of systems: state and frequency domain approaches to in® nite-dimensional systems, Lecture notes in control and information sciences (Berlin, Springer-Verlag), 185, 585-597.
22. Makila, P. M., 1990a, Approximation of stable systems by Laguerre filters. Automatica, 26, 333-345.
23. Makila, P. M., 1990b, Laguerre series approximation of infinite dimensional systems. Automatica, 26, 985-995.
24. Milkila, P. M., 1990c, Approximation and identification of continuous-time Systems. International Journal of Control, 52, 669-687.
25. Milkila, P. M., 1991, On identification of stable systems and optimal approximation. Automatica, 27, 663-676.
26. Makila, P. M., and Partington, J. R., 1993, Robust approximate modelling of stable linear systems. International Journal of Control, 58, 665-683.
27. Milkila, P. M., and Partington, J. R., 1998, Shift operator induced approximations of delay systems. Preprint.
28. Makila, P. M., Partington, J. R., and Gustafsson, T. K, 1995, Worst-case control-relevant identification. Automatica, 31, 1799-1819.
29. Mallat, S. G., and Zhang, Z., 1993, Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41, 3397-3415.
30. MeDonough, R. N., and Huggins, W. H., 1968, Best least-squares representation of signals by exponentials. IEEE Transactions on Automatic Control, AC-13, 408-412.
31. Ninness, B., and Gustafsson, F., 1997, A unifying construction of orthonormal bases for system identification. IEEE Transactions on Automatic Control, 42, 515-521.
32. Partington, J. R., 1991, Approximation of delay systems by Fourier-Laguerre series. Automatica, 27, 569-572.
33. Partington, J. R., 1997, Interpolation, Identification and Sampling (Oxford: Oxford University Press).
34. Partington, J. R., and Glover, K., 1990, Robust stabilization of delay systems by approximation of coprime factors. Systems and Control Letters, 14, 325-331.
35. x approximation and nuclearity of delay systems. Systems and Control Letters, 10, 59-65.
36. Pati, Y. C., 1992, Wavelets and time-frequency methods in linear systems and neural networks. PhD thesis, University of Maryland, College Park, MD.
37. Pati, Y. C., and Krishnaprasad, P. S., 1992, Rational wavelets in approximation and identification of stable linear systems. Proceedings of 31st IEEE Conference on Decision Control, pp. 1502-1507.
38. Petrushev, P. P., and Popov, V. A., 1987, Rational Approximation of Real Functions (Cambridge: Cambridge University Press).
39. Rosenblum, M., and Rovnyak, J. 1985, Hardy Classes and Operator Theory (Oxford: Oxford University Press).
40. Skogestad, S., and Postlethwaite, I., 1996, Multivariable Feedback Control (Chichester: Wiley).
41. Szego, G., 1975, Orthogonal Polynomials (Providence, Rhode Island: American Mathematical Society) (1st edn. 1939).
42. Wahlberg, B., and Ljung, L., 1986, Design variables for bias distribution in transfer function estimation, IEEE Transactions on Automatic Control, 31, 134-144.
43. Wahlberg, B., and Makila, P. M., 1996, On approximation of stable linear dynamical systems using Laguerre and Kautz functions. Automatica, 32, 693-708.
44. Walsh, J. L., 1935, Interpolation and Approximation by Rational Functions in the Complex Domain. (New York: American Mathematical Society).
45. Wiener, N., 1956, The Theory of Prediction. Modern Mathematics for Engineers. (New York: Bechenbach, McGraw-Hill).
46. Yoon, M. G., and Lee, B. H., 1997, A new approximation method for time-delay systems. IEEE Transactions on Automatic Control, 42, 1008-1012.
47. Zhou, K., Doyle, J. C., and Glover, K., 1996, Robust and Optimal Control. (Englewood Cliffs, NJ: Prentice-Hall).