The DOI matches its Crossref record.
Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems
Abstract
Motivated by control Lyapunov functions and Razumikhin theorems on stability of time delay systems, we introduce the concept of control Lyapunov-Razumikhin functions (CLRF). The main reason for considering CLRFs is construction of robust stabilizing control laws for time delay systems. Most existing universal formulas that apply to CLFs, are not applicable to CLRFs. It turns out that the domination redesign control law applies, achieving global practical stability and, under an additional assumption, global asymptotic stability. This additional assumption is satisfied in the practically important case when the quadratic part of a CLRF is itself a CLRF for the Jacobian linearization of the system. The CLRF based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin. While, in general, construction of CLRFs is an open problem, we show that for several classes of time delay systems a CLRF can be constructed in a systematic way.
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
Cites
No references could be resolved yet.
Research works printed but not linked: 22
- Anderson, 1990, Optimal Control: Linear Quadratic Methods
- 10.1016/0362-546x(83)90049-4 · DOI · Paper page
- 10.1109/9.739061 · doi:10.1109/9.739061
- Brockett, 1969, Finite Dimensional Linear Systems
- Freeman, 1996, Robust Control of Nonlinear Systems
- 10.1016/0005-1098(87)90072-0 · DOI
- 10.1007/978-1-4612-4342-7 · DOI · Paper page
- 10.1109/9.557574 · DOI · Paper page
- 10.1109/87.826800 · doi:10.1109/87.826800
- 10.1016/s0167-6911(99)00006-7 · doi:10.1016/s0167-6911(99)00006-7
- 10.1115/1.3653115 · DOI · Paper page
- Kolmanovsky, 1986, Stability of functional differential equations
- Kolmogorov, 1970, Introduction to Real Analysis
- Krstić, 1998, Stabilization of Nonlinear Uncertain Systems
- Krstić, 1995, Nonlinear and Adaptive Control Design
- 10.1109/TAC.1973.1100365 · DOI · Paper page
- 10.1109/9.847117 · DOI · Paper page
- 10.1007/bf01211516 · DOI · Paper page
- 10.1007/978-1-4471-0967-9 · DOI · Paper page
- 10.1016/0167-6911(89)90028-5 · DOI · Paper page
- 10.1109/9.701099 · DOI · Paper page
- 10.1109/TAC.1984.1103643 · doi:10.1109/tac.1984.1103643
Cited by
Time-delay systems: an overview of some recent advances and open problems
Richard, J.-P. (2003) · Automatica · doi:10.1016/s0005-1098(03)00167-5 · Cited by 3,353
Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems
Krstic, M. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2034923 · Cited by 393
Neural Networks-Based Adaptive Control for Nonlinear State Constrained Systems With Input Delay
Li, D.-P., Liu, Y.-J., Tong, S., Chen, C. L. P., & Li, D.-J. (2019) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2018.2799683 · Cited by 382
Approximation-based control of nonlinear MIMO time-delay systems
Ge, S. S., & Tee, K. P. (2007) · Automatica · doi:10.1016/j.automatica.2006.08.003 · Cited by 371
Backstepping Design for Time-Delay Nonlinear Systems
Mazenc, F., & Bliman, P.-A. (2006) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2005.861701 · Cited by 287
Metadata
- Authors
- Jankovic, M.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2001-07
- Volume
- 46
- Issue
- 7
- Pages
- 1048-1060
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2161450707
- Cited by
- 411
- References
- 0
- FWCI
- 16.04
- 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: Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. https://app.cochat.ai/papers/10.1109/9.935057
- The paper
- Jankovic, M. (2001). Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Transactions on Automatic Control. https://doi.org/10.1109/9.935057
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.
