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Annual Review of Control, Robotics, and Autonomous Systems

Volume 8, 2025

Using Delay for Control

  • Emilia Fridman1 and Anton Selivanov2
  • 1School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel; email: [email protected] 2School of Electrical and Electronic Engineering, University of Sheffield, Sheffield, United Kingdom; email: [email protected]
  • Vol. 8:101-126 (Volume publication date May 2025)
  • First published as a Review in Advance on November 12, 2024
  • Copyright © 2025 by the author(s).
    This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information.

Abstract

This article reviews two techniques that use delay for control: time-delay approaches to control problems (which initially may be free of delays) and the intentional insertion of delays into the feedback. We begin with a now widely used time-delay approach to sampled-data control. In networked control systems with communication constraints, this is the only method that accommodates transmission delays larger than the sampling intervals. We present a predictor-based design that enlarges the maximum allowable delay, which is important for practical implementations. We then discuss methods that use artificial delays via simple Lyapunov functionals that lead to feasible linear matrix inequalities for small delays and simple sampled-data implementations. Finally, we briefly present a new time-delay approach—this time to averaging. Unlike previous results, this approach provides the first quantitative bounds on the small parameter, making averaging-based control (including vibrational and extremum-seeking control) reliable.

Keyword(s): averaging, Lyapunov method, sampled-data control, stabilizing delay, time-delay systems
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2025-05-05
2025-06-14
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Using Delay for Control
Annual Review of Control, Robotics, and Autonomous Systems 8, 101 (2025); https://doi.org/10.1146/annurev-control-022723-033031
/content/journals/10.1146/annurev-control-022723-033031
/content/journals/10.1146/annurev-control-022723-033031
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