The DOI matches its Crossref record.
An averaging approach to chattering
Abstract
The singularly perturbed relay control systems (SPRCS) as mathematical models of chattering in the small neighborhood of the switching surface in sliding mode systems are examined. Sufficient conditions for existence and stability of fast periodic solutions to the SPRCS are found. It is shown that the slow motions in such SPRCS are approximately described by equations derived from equations for the slow variables of SPRCS by averaging along fast periodic motions. It is shown that In the general case, when the equations of a plant contain relay control nonlinearly, the averaged equations do not coincide with the equivalent control equations or with the Filippov's definition (1988) for the sliding motions in the reduced system; however, in the linear case, they coincide.
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
Levant, A. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2041973 · Cited by 482
Stability notions and Lyapunov functions for sliding mode control systems
Polyakov, A., & Fridman, L. (2014) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2014.01.002 · Cited by 420
Self-citationRubagotti, M., Raimondo, D. M., Ferrara, A., & Magni, L. (2011) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2074590 · Cited by 196
Metadata
- Authors
- Fridman, L. M.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2001
- Volume
- 46
- Issue
- 8
- Pages
- 1260-1265
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2150137810
- Cited by
- 234
- References
- 0
- FWCI
- 14.35
- 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: An averaging approach to chattering. https://app.cochat.ai/papers/10.1109/9.940930
- The paper
- Fridman, L. M. (2001). An averaging approach to chattering. IEEE Transactions on Automatic Control. https://doi.org/10.1109/9.940930
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.
