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Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model

Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model
Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model
In order to reveal the relationship between system time domain model parameters and system frequency response functions, new magnitude bounds of frequency response functions for nonlinear Volterra systems described by NARX model are established. The magnitude bound of the nth-order generalized frequency response function (GFRF) can be expressed as a simple n-degree polynomial function of the magnitude of the first order GFRF, whose coefficients are functions of the model parameters and frequency variables. Thus the system output spectrum can also be bounded by a polynomial function of the magnitude of the first order GFRF. These results demonstrate explicitly the analytical relationship between model parameters and system frequency response functions, and provide a significant insight into the magnitude based analysis and synthesis of nonlinear systems in the frequency domain.
0005-1098
838-845
Jing, Xing Jian
2fd9fcd4-7903-47a0-971d-5d26d27d4ea9
Lang, Zi Qiang
dec658e4-f38f-43fc-b094-f68c43be3105
Billings, Stephen A.
a67e1eb0-9795-42b0-9d3b-2bc158373cb2
Jing, Xing Jian
2fd9fcd4-7903-47a0-971d-5d26d27d4ea9
Lang, Zi Qiang
dec658e4-f38f-43fc-b094-f68c43be3105
Billings, Stephen A.
a67e1eb0-9795-42b0-9d3b-2bc158373cb2

Jing, Xing Jian, Lang, Zi Qiang and Billings, Stephen A. (2008) Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model. Automatica, 44 (3), 838-845. (doi:10.1016/j.automatica.2007.06.020).

Record type: Article

Abstract

In order to reveal the relationship between system time domain model parameters and system frequency response functions, new magnitude bounds of frequency response functions for nonlinear Volterra systems described by NARX model are established. The magnitude bound of the nth-order generalized frequency response function (GFRF) can be expressed as a simple n-degree polynomial function of the magnitude of the first order GFRF, whose coefficients are functions of the model parameters and frequency variables. Thus the system output spectrum can also be bounded by a polynomial function of the magnitude of the first order GFRF. These results demonstrate explicitly the analytical relationship between model parameters and system frequency response functions, and provide a significant insight into the magnitude based analysis and synthesis of nonlinear systems in the frequency domain.

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Published date: March 2008

Identifiers

Local EPrints ID: 65340
URI: http://eprints.soton.ac.uk/id/eprint/65340
ISSN: 0005-1098
PURE UUID: 9b1d4151-7576-42d0-a1b3-42c3193ae68c

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Date deposited: 12 Feb 2009
Last modified: 15 Mar 2024 12:07

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Contributors

Author: Xing Jian Jing
Author: Zi Qiang Lang
Author: Stephen A. Billings

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