Generalized frequency response function matrix for MIMO non-linear systems

International Journal of Control

Volumn 74, Issue 8, 2001, Pages 829-844

  Swain, A K ^a   Billings, S A ^a  

^a NATIONAL INSTITUTE OF TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; FREQUENCY RESPONSE; MATHEMATICAL MODELS; MATRIX ALGEBRA;

FREQUENCY RESPONSE FUNCTIONS;

NONLINEAR CONTROL SYSTEMS;

EID: 0035918732     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207170010030144     Document Type: Article

References (26)

1. Bedrosian, E., and Rice, S.O., 1971, The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian input. Proceedings of the IEEE, 59, 1688-1707.
2. Billings, S.A., 1980, Identification of nonlinear systems - a survey. Proceedings of the IEEE, Pt.D, 127, 272-285.
3. Billings, S.A., and Peyton Jones, J.C., 1990, Mapping nonlinear integro-differential equations into the frequency domain. International Journal of Control, 52, 863-879.
4. Billings, S.A., and Tsang, K.M., 1989, Spectral analysis for nonlinear systems, Part I - parametric nonlinear spectral analysis. Journal of Mechanical Systems and Signal Processing, 3, 319-339.
5. Chen, H.W., 1995, Modelling and identification of parallel nonlinear systems: structural classification and parameter estimation methods. Proceedings of the IEEE, 83, 39-66.
6. Chua, L.O., and Ng, C.Y., 1979, Frequency domain analysis of nonlinear systems: general theory. IEE Journal of Electronic Circuits and Systems, 3, 165-185.
7. Hung, G., and Stark, L., 1977, The Kernel identification methods (1910-1977)-review of theory, calculation, application and interpretation. Mathematical Bioscience, 37, 135-190.
8. Hung, G., and Stark, L., 1991, The interpretation of kernels-an overview. Annals of Biomedical Engineering, 19, 509-519.
9. Kim, K.I., and Powers, E.J., 1988, A digital method of modelling quadratically nonlinear systems with a general random input. IEEE Transactions ASSP, 36, 1758-1769.
10. Korenberg, M.J., Bruder, S.B., and Mcilroy, P.J., 1988, Exact orthogonal kernel estimation from finite data records: extending Wiener identification of nonlinear systems. Annals of Biomedical Engineering, 16, 201-214.
11. Kokenberg, M.J., and Hunter, I.W., 1990, The identification of nonlinear biological systems: Wiener approaches. Annals of Biomedical Engineering, 18, 629-654.
12. Lee, Y.W., and Schetzen, M., 1965, Measurement of Wiener kernels of a nonlinear system by cross correlation. International Journal of Control, 2, 237-254.
13. Leontaritis, I.J., and Billings, S.A., 1985, Input-output parametric models for nonlinear systems, part I - deterministic nonlinear systems. International Journal of Control, 41, 303-328.
14. Marmarelis, P.Z., and Marmarelis, V.Z., 1978, Analysis of Physiological Systems (New York: Plenum Press).
15. Marmarelis, P.Z., and Naka, K.I., 1974, Identification of multi input biological systems. IEEE Transactions on Biomedical Engineering, BME-21, 88-101.
16. Peyton Jones, J.C., and Billings, S.A., 1989, A recursive algorithm for computing the frequency response of a class of nonlinear difference equation models. International Journal of Control, 50, 1925-1940.
17. Rough, W.J., 1981, Nonlinear System Theory, the Volterra and Wiener Approach (Baltimore: John Hopkins University Press).
18. Sandberg, A., and Stark, L., 1968, Wiener and G-functional analysis as an approach to nonlinear characteristics of human pupil light reflex. Brain Research, 11, 194-211.
19. Schetzen, M., 1980, The Volterra and Wiener Theories of Nonlinear Systems (New York: Wiley).
20. Tseng, Y.C., and Linebarger, D.A., 1991, Estimating transfer functions of quadratically nonlinear systems. In Proceedings of the 25th Asilomar Conference, pp. 632-636.
21. Tseng, C.H., and Powers, E.J., 1993, Application of orthogonal search to Volterra modelling of nonlinear systems. In ICASSP-93 Proceedings, pp. 512-515.
22. Tseng, C.H., and Powers, E.J., 1995, Identification of cubic systems using higher order moments of I.I.D. signals. IEEE Transactions on Signal Processing, 43, 1733-1735.
23. Watnabe, A., and Stark, L., 1975, Kernel methods for nonlinear analysis: identification of a biological control system. Mathematical Bioscience, 27, 99-108.
24. Westwick, D.T., and Kearney, R.E., 1992, A new algorithm for identification of multi-input Wiener systems. Biological Cybernetics, 68, 75-85.
25. Worden, K., Mason, G., and Tomlinson, G.R., 1995, A harmonic probing algorithm for multi-input Volterra series. Personal communication submitted to Journal of Sound and Vibration.
26. Zhang, H., Billings, S.A., and Zhu, Q.M., 1995, Frequency response functions for nonlinear rational models, International Journal of Control, 61, 1073-1097.