Nonlinear influence in the frequency domain: Alternating series

Xingjian Jing; Zi Qiang Lang; Stephen A. Billings

doi:10.1016/j.sysconle.2011.01.003

Nonlinear influence in the frequency domain: Alternating series

Xingjian Jing, Zi Qiang Lang, Stephen A. Billings

Research output: Journal article publication › Journal article › Academic research › peer-review

49 Citations (Scopus)

Abstract

The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results.

Original language	English
Pages (from-to)	295-309
Number of pages	15
Journal	Systems and Control Letters
Volume	60
Issue number	5
DOIs	https://doi.org/10.1016/j.sysconle.2011.01.003
Publication status	Published - 1 May 2011

Keywords

Alternating series
Nonlinear systems
Output spectrum
Volterra series

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering
General Computer Science
Mechanical Engineering

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10.1016/j.sysconle.2011.01.003

Cite this

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title = "Nonlinear influence in the frequency domain: Alternating series",

abstract = "The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results.",

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AU - Billings, Stephen A.

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N2 - The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results.

AB - The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results.

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KW - Output spectrum

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JO - Systems and Control Letters

JF - Systems and Control Letters

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ER -

Nonlinear influence in the frequency domain: Alternating series

Abstract

Keywords

ASJC Scopus subject areas

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