New bound characteristics of NARX model in the frequency domain

Xingjian Jing, Z. Q. Lang, S. A. Billings

Research output: Journal article publicationJournal articleAcademic researchpeer-review

30 Citations (Scopus)


New results about the bound characteristics of both the generalized frequency response functions (GFRFs) and the output frequency response for the NARX (Non-linear AutoRegressive model with eXogenous input) model are established. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, and the coefficients of the polynomial are functions of the NARX model parameters. These new bound characteristics of the NARX model provide an important insight into the relationship between the model parameters and the magnitudes of the system frequency response functions, reveal the effect of the model parameters on the stability of the NARX model to a certain extent, and provide a useful technique for the magnitude based analysis of nonlinear systems in the frequency domain, for example, evaluation of the truncation error in a volterra series expression of non-linear systems and the highest order needed in the volterra series approximation. A numerical example is given to demonstrate the effectiveness of the theoretical results.
Original languageEnglish
Pages (from-to)140-149
Number of pages10
JournalInternational Journal of Control
Issue number1
Publication statusPublished - 1 Jan 2007
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


Dive into the research topics of 'New bound characteristics of NARX model in the frequency domain'. Together they form a unique fingerprint.

Cite this