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On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems
Abstract
This paper focuses on 'mixed' delay-independent/delay-dependent asymptotic stability problems of a class of linear systems described by delay-differential equations involving several constant but unknown delays. We give some sufficient conditions for characterizing unbounded stability regions in the delays parameter space. The proposed approach makes use of some appropriate Liapunov-Krasovskii functionals, and the results obtained are expressed in terms of matrix inequalities. We also discuss several ways to construct such analytic functionals. These results allow us to recover (or to improve) as limit cases previous delay-independent or/and delay-dependent conditions from the control literature.
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Citations
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
An integral inequality in the stability problem of time-delay systems
Gu, K. (2002) · Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) · doi:10.1109/cdc.2000.914233 · Cited by 1,543
New Lyapunov–Krasovskii functionals for stability of linear retarded and neutral type systems
Fridman, E. (2001) · Systems & Control Letters · doi:10.1016/s0167-6911(01)00114-1 · Cited by 915
Li, T., Shang, P., & Diagne, M. (2026) · Automatica · doi:10.1016/j.automatica.2026.113282
Metadata
- Authors
- Kolmanovskii, V. B.
- Venue
- International Journal of Control
- Publisher
- Informa UK Limited
- Published
- 1999-01
- Volume
- 72
- Issue
- 4
- Pages
- 374-384
- ISSN
- 0020-7179 (ISSN-L)
- 1366-5820
- OpenAlex
- W2002430999
- Cited by
- 200
- References
- 0
- FWCI
- 34.47
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems. https://app.cochat.ai/papers/10.1080/002071799221172
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- Kolmanovskii, V. B. (1999). On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems. International Journal of Control. https://doi.org/10.1080/002071799221172
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