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

Xingjian Jing, Zi Qiang Lang, Stephen A. Billings

Research output: Journal article publicationJournal articleAcademic researchpeer-review

26 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)838-845
Number of pages8
JournalAutomatica
Volume44
Issue number3
DOIs
Publication statusPublished - 1 Mar 2008
Externally publishedYes

Keywords

  • Generalized frequency response function (GFRF)
  • Magnitude bounds
  • NARX model
  • Nonlinear systems
  • Volterra series

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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