Cited by 229Stability and Control of Uncertain SystemsAdvanced Control Systems OptimizationNeural Networks Stability and Synchronization

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Compensation of State-Dependent Input Delay for Nonlinear Systems

Bekiaris-Liberis, Nikolaos, Krstic, Miroslav·2013·IEEE Transactions on Automatic Control

DOI 10.1109/tac.2012.2208294

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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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Authors: Bekiaris-Liberis, N., & Krstic, M.
Affiliations: University of California San Diego (US)
ORCID: Bekiaris-Liberis, Nikolaos
Venue: IEEE Transactions on Automatic Control
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 2013-02
Volume: 58
Issue: 2
Pages: 275-289
ISSN: 0018-9286 (ISSN-L)
1558-2523
DOI: 10.1109/tac.2012.2208294
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
Licence: ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
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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Compensation of State-Dependent Input Delay for Nonlinear Systems

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