The DOI matches its OpenAlex record.
Representations of non-linear systems: the NARMAX model
Abstract
Input-output representations of non-linear discrete-time systems are discussed. It is shown that the NARMAX (Non-linear AutoRegressive Moving Average with eXogenous inputs) model is a general and natural representation of non-linear systems and contains, as special cases, several existing non-linear models. The problem of approximating non-linear input-output systems is also addressed and several properties of non-linear models are highlighted using simple examples.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Practical identification of NARMAX models using radial basis functions
CHEN, S., BILLINGS, S. A., COWAN, C. F. N., & GRANT, P. M. (1990) · International Journal of Control · doi:10.1080/00207179008953599 · Cited by 306
Self-citationA review of nonlinear dynamics applications to structural health monitoring
Worden, K., Farrar, C. R., Haywood, J., & Todd, M. (2008) · Structural Control and Health Monitoring · doi:10.1002/stc.215 · Cited by 212
Peng, Z. K., Lang, Z. Q., Wolters, C., Billings, S. A., & Worden, K. (2011) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2010.09.014 · Cited by 111
Self-citation
Metadata
- Authors
- Chen, S., & Billings, S. A.
- Venue
- International Journal of Control
- Publisher
- Taylor & Francis
- Published
- 1989-01-01
- Volume
- 49
- Issue
- 3
- Pages
- 1013-1032
- ISSN
- 0020-7179 (ISSN-L)
- OpenAlex
- W2028847290
- Cited by
- 903
- References
- 0
- FWCI
- 14.08
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Representations of non-linear systems: the NARMAX model. https://app.cochat.ai/papers/10.1080/00207178908547379
- The paper
- Chen, S., & Billings, S. A. (1989). Representations of non-linear systems: the NARMAX model. International Journal of Control. https://doi.org/10.1080/00207178908547379
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
