A bound for the magnitude characteristics of nonlinear output frequency response functions Part 1. Analysis and computation

International Journal of Control

Volumn 65, Issue 2, 1996, Pages 309-328

  Billings, S A ^a   Lang, Zi Qiang ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; CONTROL NONLINEARITIES; CONTROL SYSTEM ANALYSIS; FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS;

MAGNITUDE FREQUENCY DOMAIN CHARACTERISTICS; NONLINEAR OUTPUT FREQUENCY RESPONSE FUNCTIONS; POLYNOMIAL NONLINEAR AUTOREGRESSIVE MODEL;

FREQUENCY RESPONSE;

EID: 0030244598     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207179608921699     Document Type: Article

References (19)

1. Bedrosian, E., and Rice, S. O., 1971, The output properties of Volterra systems driven by harmonic and gaussian inputs. Proceedings of the Institute of Electrical and Electronics Engineers, 59, 1688-1707.
2. Billings, S. A., and Lang, Zi-Qiang, 1996, A bound for the magnitude characteristics of nonlinear output frequency response functions-Part 2: Practical computation of the bound for systems described by the nonlinear autoregressive model with exogenous input. International Journal of Control, 65, 365-384.
3. Billings, S. A., and Peyton Jones, J. C., 1990, Mapping nonlinear integro-diflerential equation into the frequency domain. International Journal of Control, 52, 863-879.
4. Billings, S. A., and Tsang, K. M., 1989a, Spectral analysis for nonlinear systems, Part 1: Parametric nonlinear spectral analysis. Mechanical Systems and Signal Processing, 3, 319-339
5. Billings, S. A., Tsang, K. M., and Tomlinson, G. R., 1990, Spectral analysis for nonlinear systems, Part 111: Case study examples. Mechanical Systems and Signal Processing, 4, 3-21.
6. Billings, S. A. and Yusof, M. I., 1996, Decomposition of generalised frequency response functions for nonlinear systems using symbolic computation. International Journal of Control, 65, to be published.
7. Bussgang, J. J., Ehrman, L., and Garham, J. W., 1974, Analysis of nonlinear systems with multiple inputs. Proceedings of the Institute of Electrical and Electronics Engineers, 62, 1088-1119.
8. Chen, S., and Billings, S. A., 1989, Representation of nonlinear systems: the NARMAX model. International Journal of Control, 49, 1013-1032.
9. Cho, Y. S., Kim, S. D., Hixson, E. L., and Powers, E. J., 1992, A digital technique to estimate second order distortion using higher order coherence spectra, IEEE Transactions on Acoustics, Speech and Signal Processing, 40, 1029-1040.
10. Glenn, Z., and Fred, J. T., 1994, Advanced Digital Signal Processing (New York: Marcel Dekker), pp, 87-102.
11. James, G., and James, R. C., 1959, Mathematics Dictionary (Princeton, New Jersey, U.S.A.: Van Nostrand), p. 248.
12. Lang, Z.-Q., and Billings, S. A., 1996, Output frequency characteristics of nonlinear systems. International Journal of Control, 64, 1049-1067.
13. Kim, K. I., and Powers, E. J., 1988, A digital method of modelling quadratically nonlinear systems with a general random input. IEEE Transactions on Acoustics, Speech and Signal Processing, 36, 1758-1759.
14. 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, 1925-1949.
15. Powers, E. J., and Miksad, R. W., 1987, Polyspectral measurement and analysis of nonlinear wave interactions. Proceedings of the Symposium on Nonlinear Wave Interactions in Fluids, pp. 9-16.
16. Spiegel, R., 1974, Theory and Problems of Advanced Calculus. SI (metric) edition, Schaums Outline Series (New York: McGraw-Hill), Chapter 10, pp. 198-199.
17. Vinh, T., Chouychai, T., Liu, H., and Diouder, M., 1987, Second order transfer function: computation and physical interpretation. Proceedings of the Fifth International Model Analysis Conference, London, U.K., pp. 587-592.
18. Worden, K., Stansby, P. K., Tomlinson, G. R., and Billings, S. A., 1994, Identification of nonlinear wave forces. Journal of Fluids and Structures, 8, 19-71.
19. Zhang, H., Billings, S. A., and Zhu, Q. M., 1995, Frequency response functions for nonlinear rational models. International Journal of Control, 61, 1073-1097.