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Compensation of State-Dependent Input Delay for Nonlinear Systems
Abstract
We introduce and solve stabilization problems for linear and nonlinear systems with state-dependent input delay. Since the state dependence of the delay makes the prediction horizon dependent on the future value of the state, which means that it is impossible to know a priori how far in the future the prediction is needed, the key design challenge is how to determine the predictor state. We resolve this challenge and establish closed-loop stability of the resulting infinite-dimensional nonlinear system for general non-negative-valued delay functions of the state. Due to an inherent limitation on the allowable delay rate in stabilization of systems with time-varying input delays, in the case of state-dependent delay, where the delay rate becomes dependent on the gradient of the delay function and on the state and control input, only regional stability results are achievable. For forward-complete systems, we establish an estimate of the region of attraction in the state space of the infinite-dimensional closed-loop nonlinear system and for linear systems we prove exponential stability. Global stability is established under a restrictive Lyapunov-like condition, which has to be a priori verified, that the delay rate be bounded by unity, irrespective of the values of the state and input. We also establish local asymptotic stability for locally stabilizable systems in the absence of the delay. Several illustrative examples are provided, including unicycle stabilization subject to input delay that grows with the distance from the reference position.
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“Equation (31) indicates that system (1)-(3) is no longer equivalent to the following classical time-delay system in [5,6,14-17]”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [6]
In the citing paper
“Our controller incorporates a compensator that effectively cancels the influence of inhomogeneous terms in the PDE actuator state, without imposing any restrictions on the severity of the nonlinearity or the feasibility condition [5,6], while guaranteeing the latter through an assumption on the positivity of the transport speed to avoid an illposed problem (see [14,17]).”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [6]
Citations
Cites
(2000) · University of Maribor digital library (University of Maribor) · Cited by 9,354
A Survey of Recent Results in Networked Control Systems
Hespanha, J. P., Naghshtabrizi, P., & Xu, Y. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887288 · Cited by 3,816
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
Traffic and related self-driven many-particle systems
Helbing, D. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.1067 · Cited by 3,285
On characterizations of the input-to-state stability property
Sontag, E. D., & Wang, Y. (1995) · Systems & Control Letters · doi:10.1016/0167-6911(94)00050-6 · Cited by 1,793
Delay Effects on Stability. A Robust Control Approach
Niculescu, S. (2001) · HAL (Le Centre pour la Communication Scientifique Directe) · doi:10.1007/1-84628-553-4 · Cited by 1,419
Finite spectrum assignment problem for systems with delays
Manitius, A., & Olbrot, A. (1979) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1979.1102124 · Cited by 1,140
Linear systems with delayed controls: A reduction
Artstein, Z. (1982) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1982.1103023 · Cited by 1,113
Stability and Stabilization of Time-Delay Systems
Michiels, W., & Niculescu, S. (2007) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718645 · Cited by 727
A characterization of integral input-to-state stability
Angeli, D., Sontag, E. D., & Wang, Y. (2000) · IEEE Transactions on Automatic Control · doi:10.1109/9.863594 · Cited by 663
Pomet, J. (1992) · Systems & Control Letters · doi:10.1016/0167-6911(92)90019-o · Cited by 598
Robust Control of Time-delay Systems
(2006) · Springer eBooks · doi:10.1007/1-84628-265-9 · Cited by 475
Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem
Teel, A. R. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.701099 · Cited by 462
Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems
Janković, M. (2001) · IEEE Transactions on Automatic Control · doi:10.1109/9.935057 · Cited by 408
Forward completeness, unboundedness observability, and their Lyapunov characterizations
Angeli, D., & Sontag, E. D. (1999) · Systems & Control Letters · doi:10.1016/s0167-6911(99)00055-9 · Cited by 398
Finite spectrum assignment of unstable time-delay systems with a safe implementation
Mondié, S., & Michiels, W. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.820147 · Cited by 394
Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems
Krstić, M. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2034923 · Cited by 393
A Lyapunov–Krasovskii methodology for ISS and iISS of time-delay systems
Pepe, P., & Jiang, Z.-P. (2006) · Systems & Control Letters · doi:10.1016/j.sysconle.2006.06.013 · Cited by 364
Lyapunov Stability of Linear Predictor Feedback for Time-Varying Input Delay
Krstić, M. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2038196 · Cited by 312
Analytical Stability Prediction and Design of Variable Pitch Cutters
Altıntaş, Y., Engin, Ş., & Budak, E. (1999) · Journal of Manufacturing Science and Engineering · doi:10.1115/1.2831201 · Cited by 278
Adaptive trajectory tracking despite unknown input delay and plant parameters
Bresch‐Pietri, D., & Krstić, M. (2009) · Automatica · doi:10.1016/j.automatica.2009.04.027 · Cited by 260
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
Backstepping design for time-delay nonlinear systems
Mazenc, F., & Bliman, P. (2006) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2005.861701 · Cited by 238
Krstić, M. (2008) · Automatica · doi:10.1016/j.automatica.2008.04.010 · Cited by 237
Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $
Bresch‐Pietri, D., & Krstić, M. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2050352 · Cited by 202
Mahaffy, J. M., Bélair, J., & Mackey, M. C. (1998) · Journal of Theoretical Biology · doi:10.1006/jtbi.1997.0537 · Cited by 192
Sipahi, R., Atay, F. M., & Niculescu, S. (2007) · SIAM Journal on Applied Mathematics · doi:10.1137/060673813 · Cited by 191
Further results on input-to-state stability for nonlinear systems with delayed feedbacks
Mazenc, F., Malisoff, M., & Lin, Z. (2008) · Automatica · doi:10.1016/j.automatica.2008.01.024 · Cited by 162
An adaptive Smith-controller for time-delay systems with relative degree
Niculescu, S., & Annaswamy, A. M. (2003) · Systems & Control Letters · doi:10.1016/s0167-6911(03)00113-0 · Cited by 158
Deadtime compensation for nonlinear processes
Kravaris, C., & Wright, R. A. (1989) · AIChE Journal · doi:10.1002/aic.690350914 · Cited by 157
Beyond Webcams: An Introduction to Online Robots
(2003) · Sensor Review · doi:10.1108/sr.2003.08723cae.002 · Cited by 139
Subcritical Hopf bifurcations in a car-following model with reaction-time delay
Orosz, G., & Stépàn, G. (2006) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2006.1660 · Cited by 137
Finite-Time Global Stabilization by Means of Time-Varying Distributed Delay Feedback
Karafyllis, I. (2005) · Proceedings of the 44th IEEE Conference on Decision and Control · doi:10.1137/040616383 · Cited by 131
On the approximation of distributed-delay control laws
Mirkin, L. (2003) · Systems & Control Letters · doi:10.1016/j.sysconle.2003.09.010 · Cited by 123
Boundary layer phenomena for differential-delay equations with state-dependent time lags, I.
Mallet‐Paret, J., & Nussbaum, R. D. (1992) · Archive for Rational Mechanics and Analysis · doi:10.1007/bf00418497 · Cited by 119
Stabilization 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
Analytical approximation of open-channel flow for controller design
Litrico, X., & Fromion, V. (2004) · Applied Mathematical Modelling · doi:10.1016/j.apm.2003.10.014 · Cited by 116
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
Stabilization by Means of Approximate Predictors for Systems with Delayed Input
Karafyllis, I. (2011) · SIAM Journal on Control and Optimization · doi:10.1137/100781973 · Cited by 101
On Compensating Long Actuator Delays in Nonlinear Control
Krstić, M. (2008) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2008.928123 · Cited by 100
Adaptive posicast controller for time-delay systems with relative degree n∗≤2
Yıldız, Y., Annaswamy, A. M., Kolmanovsky, I. V., & Yanakiev, D. (2009) · Automatica · doi:10.1016/j.automatica.2009.11.008 · Cited by 99
Forwarding, backstepping, and finite spectrum assignment for time delay systems
Janković, M. (2008) · Automatica · doi:10.1016/j.automatica.2008.04.021 · Cited by 98
Recursive predictor design for state and output feedback controllers for linear time delay systems
Janković, M. (2010) · Automatica · doi:10.1016/j.automatica.2010.01.021 · Cited by 96
Remote Stabilization Via Communication Networks With a Distributed Control Law
Witrant, E., de Wit, C. C., Georges, D., & Alamir, M. (2007) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.902757 · Cited by 88
Flatness-based control of nonlinear delay systems: A chemical reactor example
Mounier, H., & Rudolph, J. (1998) · International Journal of Control · doi:10.1080/002071798221614 · Cited by 85
Pepe, P., Karafyllis, I., & Jiang, Z. (2008) · Automatica · doi:10.1016/j.automatica.2008.01.010 · Cited by 81
Delayed Feedback Control near Hopf BifurcationPreprint
Atay, F. M. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0812.4687 · Cited by 77
Lyapunov theorems for systems described by retarded functional differential equations
Karafyllis, I. (2005) · Nonlinear Analysis · doi:10.1016/j.na.2005.04.045 · Cited by 73
Generating positive and stable solutions through delayed state feedback
Mazenc, F., & Niculescu, S. (2011) · Automatica · doi:10.1016/j.automatica.2011.01.029 · Cited by 70
Karafyllis, I., Pepe, P., & Jiang, Z. (2009) · Nonlinear Analysis · doi:10.1016/j.na.2009.01.244 · Cited by 66
Finite pole assignment for systems with time-varying input delays
Nihtilä, M. T. (2002) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.1991.261456 · Cited by 60
Control of integral processes with dead-time. Part 2: Quantitative analysis
Zhong, Q., & Mirkin, L. (2002) · IEE Proceedings - Control Theory and Applications · doi:10.1049/ip-cta:20020439 · Cited by 59
Nonuniform in Time Input-to-State Stability and the Small-Gain Theorem
Karafyllis, I., & Tsinias, J. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.822861 · Cited by 56
Cross-Term Forwarding for Systems With Time Delay
Janković, M. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2012978 · Cited by 50
Adaptive control of a continuous-time system with time-varying input delay
Nihtilä, M. T. (1989) · Systems & Control Letters · doi:10.1016/0167-6911(89)90046-7 · Cited by 47
Stabilization of a chemostat model with Haldane growth functions and a delay in the measurements
Mazenc, F., & Malisoff, M. A. (2010) · Automatica · doi:10.1016/j.automatica.2010.06.012 · Cited by 43
Pitfalls in the fluid modeling of RTT variations in window-based congestion control
Liu, S., Başar, T., & Srikant, R. (2005) · doi:10.1109/infcom.2005.1498329 · Cited by 32
Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow
Hansen, M. R., Stoustrup, J., & Bendtsen, J. D. (2011) · IFAC Proceedings Volumes · doi:10.3182/20110828-6-it-1002.01947 · Cited by 19
Sipahi, R., Lämmer, S., Helbing, D., & Niculescu, S. (2006) · doi:10.1115/imece2006-14782 · Cited by 14
Stabilization By Means of Approximate Predictors for Systems with Delayed Input
Karafyllis, I. (2010) · IFAC Proceedings Volumes · doi:10.3182/20100607-3-cz-4010.00004 · Cited by 9
Flagged first, then by citations
Research works printed but not linked: 3
- khalil, 2002, Nonlinear Systems
- sipahi, 2007, Delay modeling in supply network dynamics Performance synchronization stability
- niculescu, 2001, Delay Effects on Stability
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Stability of nonlinear differential systems with state-dependent delayed impulses
Li, X., & Wu, J. (2015) · Automatica · doi:10.1016/j.automatica.2015.10.002 · Cited by 346
Exponential stability of nonlinear state-dependent delayed impulsive systems with applications
Xu, Z., Li, X., & Stojanović, V. (2021) · Nonlinear Analysis Hybrid Systems · doi:10.1016/j.nahs.2021.101088 · Cited by 152
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Metadata
- Authors
- Bekiaris-Liberis, N., & Krstic, M.
- Affiliations
- University of California San Diego (US)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2013-02
- Volume
- 58
- Issue
- 2
- Pages
- 275-289
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2022076727
- Cited by
- 229
- References
- 60
- Citations by year
- 2026: 4 · 2025: 9 · 2024: 4 · 2023: 14 · 2022: 22 · 2021: 16 · 2020: 12 · 2019: 13 · 2018: 19 · 2017: 28 · 2016: 22 · 2015: 26 · 2014: 19 · 2013: 18
- FWCI
- 30.56
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Physical Sciences › Engineering › Control and Systems Engineering › Neural Networks Stability and Synchronization
- Keywords
- time-varying input delay, nonlinear systems, linear systems, closed-loop stability, regional stability, domain of attraction, exponential stability, local asymptotic stability
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