A Halanay Approach for Compensating Unknown Time-Varying Delays via Instantaneous Universal Controllers
Abstract
This letter proves that the universal control scheme proposed in [20] by instantaneous state feedback is also capable of dealing with certain linearly growth systems withunknown time-varying delaysin state/input. The proof is carried out by developing a Lyapunov-Halanay approach which makes it possible to compensate unknown time-varying delays that are piecewise continuous and dominated by anunknown constant, but also to remove the condition that ˙di(t) ≤ δ0, typically required in the LK-functional method.
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Stability of Time-Delay Systems
Gu, K., Kharitonov, V., & Chen, J. (2003) · Control engineering · doi:10.1007/978-1-4612-0039-0 · Cited by 4,471 · see citing works
Adaptive control of nonlinearly parameterized systems: the smooth feedback case
Lin, W. T., & Qian, C. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2002.800773 · Cited by 632 · see citing works
Self-citationAdaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework
Lin, W., & Qian, C. (2002) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2002.1000270 · Cited by 394 · see citing works
Self-citationUniversal adaptive control of nonlinear systems with unknown growth rate by output feedback
Hao, L., & Lin, W. T. (2006) · Automatica · doi:10.1016/j.automatica.2006.05.006 · Cited by 308 · see citing works
Self-citationStability, Control, and Computation for Time-Delay Systems
(2014) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611973631 · Cited by 283 · see citing works
Global Asymptotic Stabilization of Feedforward Systems With Delay in the Input
Mazenc, F., Mondié, S., & Francisco, R. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.828313 · Cited by 257 · see citing works
Global asymptotic stabilization for chains of integrators with a delay in the input
Mazenc, F., Mondié, S., & Niculescu, S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2002.806654 · Cited by 253 · see citing works
Global adaptive stabilization in the absence of information on the sign of the high frequency gain
Willems, J. C., & Byrnes, G. I. (2005) · Springer eBooks · doi:10.1007/bfb0004944 · Cited by 232 · see citing works
Stabilizing a Chain of Integrators Using Multiple Delays
Niculescu, S., & Michiels, W. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.828326 · Cited by 222 · see citing works
Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach
Hao, L., & Lin, W. T. (2007) · Systems & Control Letters · doi:10.1016/j.sysconle.2007.03.002 · Cited by 174 · see citing works
Self-citationStabilization of linear strict-feedback systems with delayed integrators
Bekiaris-Liberis, N. K., & Krstić, M. (2010) · Automatica · doi:10.1016/j.automatica.2010.07.008 · Cited by 118 · see citing works
Delay-adaptive feedback for linear feedforward systems
Bekiaris-Liberis, N. K., & Krstić, M. (2010) · Systems & Control Letters · doi:10.1016/j.sysconle.2010.03.001 · Cited by 107 · see citing works
Zhao, C., & Lin, W. T. (2020) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.3021053 · Cited by 55 · see citing works
Self-citationThe ISS framework for time-delay systems: a survey
Chaillet, A., Karafyllis, I., Pepe, P., & Wang, Y. (2023) · Mathematics of Control Signals and Systems · doi:10.1007/s00498-023-00341-w · Cited by 52 · see citing works
Sun, J., & Lin, W. T. (2020) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2020.3030744 · Cited by 39 · see citing works
Self-citationA nonlinear version of Halanay's inequality for the uniform convergence to the origin
Pepe, P. (2021) · Mathematical Control and Related Fields · doi:10.3934/mcrf.2021045 · Cited by 26 · see citing works
Stabilization of chains of linear parabolic PDE–ODE cascades
Xu, X., Liu, L., Krstić, M., & Feng, G. (2022) · Automatica · doi:10.1016/j.automatica.2022.110763 · Cited by 25 · see citing works
Niu, X., Lin, W. T., & Gao, X. (2021) · Automatica · doi:10.1016/j.automatica.2020.109457 · Cited by 21 · see citing works
Self-citationSun, J., & Lin, W. T. (2023) · Systems & Control Letters · doi:10.1016/j.sysconle.2023.105456 · Cited by 15 · see citing works
Self-citationYu, X., & Lin, W. T. (2024) · Automatica · doi:10.1016/j.automatica.2024.111969 · Cited by 8 · see citing works
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Research works printed but not linked: 2
- Halanay, 1966, Differential Equations, Stability, Oscillations, Time Lags
- Yu, 2026, A dynamic extension method for output feedback control of uncertain systems with unknown time-varying delays
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- Authors
- Yu, X., & Lin, W.
- Affiliations
- Jiangsu Normal University (CN)
- Case Western Reserve University (US)
- Venue
- IEEE Control Systems Letters
- Published
- 2026
- Volume
- 10
- Pages
- 739-744
- ISSN
- 2475-1456 (ISSN-L)
- OpenAlex
- W7164398129
- Cited by
- 0
- References
- 20
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Control Systems Letters (publishedVersion)
- Funders
- NSF (62473178, 62173161)
- Qing Lan Project of Jiangsu Province, China.
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Computer Science › Computer Networks and Communications › Neural Networks Stability and Synchronization
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Keywords
- Halanay inequality, unknown time-varying delays, state feedback, time delay compensation
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