Some frequency-domain approaches to the model reduction of delay systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 36, Issue 19, 2003, Pages 1-9

  Partington, Jonathan R ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Delay system; Fourier series; Frequency domain; Hankel operator; Inner function; Model reduction; Pade approximant; Wavelet

Indexed keywords

DELAY CONTROL SYSTEMS; ERROR ANALYSIS; FOURIER SERIES; HANKEL FUNCTIONS; MATRIX ALGEBRA;

DELAY SYSTEMS; FREQUENCY DOMAINS; HANKEL OPERATORS; INNER FUNCTIONS; MODEL REDUCTION; PADE APPROXIMANTS; WAVELET;

FREQUENCY DOMAIN ANALYSIS;

EID: 85047014548     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1016/S1474-6670(17)33294-9     Document Type: Conference Paper

References (41)

1. Adamjan, V. M., D. Z. Arov and M. G. KreTn (1971). Analytic propenies of the Schmidt pairs of a Hankel operator and the generalized SchurTakagi problem. Mat. Sb. (N.S.) 86(128), 34-75.
2. Bellman, R., K. L. Cooke (1963). Differentialdifference equations. Academic Press. New York.
3. Cunain, R. F., H. Zwan (1995). An introduction to infinite-dimensional linear systems theory. Springer-Verlag. New York. Dudley Ward, N. F., 1.
4. R. Panington (1995). Rational wavelet decompositions of transfer functions in Hardy-Sobolev classes. Math. Control Signals Systems 8(3), 257-278.
5. Enns, D. (1984). Model reduction for control system design. Ph.D. dissenation. Stanford University.
6. Glader, C, G. Hognas, P. M. MakiIa and H. T. Toivonen (1991). Approximation of delay systems-A case study. Internat. J. Control 53(2), 369-390.
7. Glover, K. (1984). All optimal Hankel-norm approximations of linear multivariable systems and their L-error bounds. Internat. J. Control 39(6),1115-1193.
8. Glover, K., J. R. Panington (1987). Bounds on the achievable accuracy in model reduction. In: Modelling, robustness and sensitivity reduction in control systems (Groningen, 1986). pp. 95118. Springer. Berlin.
9. Glover, K., J. Lam and J. R. Panington (1990). Rational approximation of a class of infinitedimensional systems. I. Singular values of Hankel operators. Math. Control Signals Systems 3(4),325-344.
10. Glover, K., J. Lam and J. R. Panington (l99Ia). Rational approximation of a class of infinitedimensional systems. 11. Optimal convergence rates of L- A pproximants. Math. Control Signals Systems 4(3), 233-246.
11. Glover, K., J. Lam and J. R. Panington (l99Ib). Rational approximation of a class of infinitedimensional systems: The L2 case. In: Progress in approximation theory. pp. 405-440. Academic Press. Boston, MA.
12. Glover, K., R. F. Cunain and J. R. Panington (1988). Realisation and approximation of linear infinitedimensional systems with error bounds. SIAM J. ControlOptim. 26(4), 863-898.
13. Gu, G., P. P. Khargonekar and E. B. Lee (1989). Approximation of infinite-dimensional systems. IEEE Trans. Automat. Control 34(6), 610-618.
14. Gu, G., P. P. Khargonekar, E. B. Lee and P. Misra (1992). Finite-dimensional approximations of unstable infinite-dimensional systems. SIAM J. ControlOptim. 30(3), 704-716.
15. Makila, P. M. (l990a). Approximation and identification of continuous-time systems. Internat. J. Control 52(3), 669-687.
16. MakiIa, P. M. (l990b). Approximation of stable systems by Laguerre filters. Automatica J. IFAC 26(2),333-345.
17. Makila, P. M. (l990c). Laguerre series approximation of infinite-dimensional systems. Automatica J. IFAC 26(6), 985-995.
18. Makila, P. M., J. R. Panington (l999a). Laguerre and Kautz shift approximations of delay systems. Illlernat. J. Control 72( 10), 932-946.
19. Makila, P. M., 1. R. Panington (l999b). Shift operator induced approximations of delay systems. SIAM J. ControlOptim 37(6), 1897-1912.
20. Mallat, S. G., Z. F. Zhang (1993). Matching pursuits with time-frequency dictionaries. 1EEE Trans. Signal Process. 41, 3397-3415.
21. Moore, B. C (1981). Principal component analysis in linear systems: Controllability, observability, model reduction. IEEE Trans. Automat. Control 26(1),17-32.
22. Nikolski, N. K. (2002). Operators. junctions, systems: An easy reading. Vo/. 1. Vo\. 92 of Mathematical Surveys and Monographs. American Mathematical Society.
23. Providence, RI. Panington, J. R. (1988). An introduction to Hankel operators. Cambridge University Press. Cambridge.
24. Partington, J. R. (1991a). Approximation of delay systems by Fourier-Laguerre series. Automatica J. IFAC 27(3), 569-572.
25. Panington, J. R. (1991b). Approximation of unstable infinite-dimensional systems using coprime factors. Systems Control Lelt. 16(2), 89-96.
26. Panington, J. R (2003). Model reduction of delay systems. In: Sixty open problems in the mathematics of systems and control (V. D. Blondel and A. Megretski, Eds.). Princeton University Press. To appear.
27. Partington, J. R., K. Glover (1990). Robust stabilization of delay systems by approximation of coprime factors. Systems Control Lett. 14(4), 325331.
28. Panington, J. R., K. Glover, H. J. Zwan and R. F. Curtain (1988). L- A pproximation and nuclearity of delay systems. Systems Control Lelt. 10(1), 5965.
29. Pati, Y. C, R. Rezaiifar, P.S. Krishnaprasad and WP. Dayawansa (1993). A fast recursive algorithm for system identification and model reduction using rational wavelets. Proc. 27th Asilomar ConI
30. Peller, V. V. (2003). Hankel operators and their applications. Springer Monographs in Mathematics. Springer-Verlag. New York.
31. Pernebo, L., L. M. Silverman (1982). Model reduction via balanced state space representations. IEEE Trans. Automat. Control 27(2), 382-387.
32. Perron, O. (1913). Die Lehre von den Kettenbriichen. B. G. Teubner. Leipzig.
33. Power, S. C (1982). Hankel operators on Hilben space. Pitman (Advanced Publishing Program). Boston, Mass.
34. Saff, E. B., R. S. Varga (1975/76). On the zeros and poles of Pade approximants to c. Numer. Math. 25(1),1-14.
35. Trefethen, L. N. (1981). Rational Chebyshev approximation on the unit disk. Numer. Math. 37(2),297-320.
36. van Rossum, H. (1971). On the poles of Pade approximations to C. Nieuw Arch. Wisk. (3) 19,37-45.
37. Wahlberg, B., P. M. Makila (1996). On approximation of stable linear dynamical systems using La guerre and Kautz functions. Automatica J. IFAC 32(5),693-708.
38. Walsh, J. L. (1965). Interpolation and approximation by rational functions in the complex domain. Fourth edition. American Mathematical Society Colloquium Publications, Vo. XX. American Mathematical Society. Providence, R.1.
39. Zervos, c., P. R. Belanger and G. A. Dumont (1988). On PID controller tuning using orthonorrnal series identification. Auromatica 24, 165-175.
40. Zhou, K., J. C. Doyle and K. Glover (1996). Robust and optimal control. Prentice Hall. Upper Saddle River, N1.
41. Zwart, H. 1., R. F. Curtain, 1. R. Partington and K. Glover (1988). Partial fraction expansions for delay systems. Systems Control Left. 10(4),235243.