Quantization, Time Delays, and Nonlinear Stabilization
Abstract
The purpose of this note is to demonstrate that a unified study of quantization and delay effects in nonlinear control systems is possible by merging the quantized feedback control methodology recently developed by the author and the small-gain approach to the analysis of functional differential equations with disturbances proposed earlier by Teel. We prove that under the action of a robustly stabilizing feedback controller in the presence of quantization and time delays satisfying suitable conditions, solutions of the closed-loop system starting in a given region remain bounded and eventually enter a smaller region. We present several versions of this result and show how it enables global asymptotic stabilization via a dynamic quantization strategy.
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Simultaneous compensation of long input delays and quantization effects in nonlinear systems is a problem of theoretical and practical significance that has not been addressed before.
“Thus, simultaneous compensation of long input delays and quantization effects in nonlinear systems is a problem of theoretical and practical significance, which has not been, heretofore, addressed.”
From Semiglobal Switched Predictor-Feedback Stabilization of Nonlinear Systems With Input Delay and State/Input Quantization (2026) · cites this paper as [28]
The design and stability analysis do not explicitly depend on the generalized solutions interpretation, as also noted in [27], [28] for ODE systems, on which the well-posedness proof essentially relies via the predictor state P.
“We note that our design and stability analysis do not explicitly depend on such generalized solutions interpretation, as also noted in [27], [28] for the case of ODE systems, on which our well-posedness proof, essentially, relies (via considering the predictor state P ).”
From Semiglobal Switched Predictor-Feedback Stabilization of Nonlinear Systems With Input Delay and State/Input Quantization (2026) · cites this paper as [28]
Cited by
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Liu, W., Ma, Q., & Xu, S. (2024) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2024.3360281 · Cited by 24 · see citing works
Koudohode, F., & Bekiaris-Liberis, N. (2026) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2026.3730335
- Authors
- Liberzon, D.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Corresponding author
- Liberzon, D.
- ORCID
- Liberzon, D.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2006-07
- Volume
- 51
- Issue
- 7
- Pages
- 1190-1195
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2131759005
- Cited by
- 196
- References
- 0
- Citations by year
- 2026: 12 · 2025: 12 · 2024: 10 · 2023: 14 · 2022: 6 · 2021: 10 · 2020: 5 · 2019: 3 · 2018: 8 · 2017: 4 · 2016: 7 · 2015: 5 · 2014: 11 · 2013: 10 · 2012: 9
- FWCI
- 34.31
- 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 Design
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Keywords
- quantized feedback control, time delay, nonlinear stabilization, functional differential equations, robust stabilization, global asymptotic stabilization, dynamic quantization, boundedness of solutions
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