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A survey on Lyapunov-based methods for stability of linear time-delay systems

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Abstract

Recently, stability analysis of time-delay systems has received much attention. Rich results have been obtained on this topic using various approaches and techniques. Most of those results are based on Lyapunov stability theories. The purpose of this article is to give a broad overview of stability of linear time-delay systems with emphasis on the more recent progress. Methods and techniques for the choice of an appropriate Lyapunov functional and the estimation of the derivative of the Lyapunov functional are reported in this article, and special attention is paid to reduce the conservatism of stability conditions using as few as possible decision variables. Several future research directions on this topic are also discussed.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61104097, 61321002, 61120106010, 61522303, and U1509215), Program for Changjiang Scholars and Innovative Research Team in University (IRT1208), ChangJiang Scholars Program, Beijing Outstanding PhD Program Mentor (20131000704), Program for New Century Excellent Talents in University (NCET-13-0045), and Beijing Higher Education Young Elite Teacher Project.

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  1. School of Automation, Beijing Institute of Technology, Beijing, 100081, China

    Jian Sun & Jie Chen

  2. Key Laboratory of Intelligent Control and Decision of Complex System, Beijing Institute of Technology, Beijing, 100081, China

    Jian Sun & Jie Chen

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  1. Jian Sun
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Correspondence to Jian Sun.

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Jian Sun received his PhD Degree from the Institute of Automation, Chinese Academy of Sciences, China in 2007. He is currently a professor in the School of Automation, Beijing Institute of Technology, China. His current research interests include networked control systems, timedelay systems, security of CPSs, and robust control. He is the awardee of the NSFC Excellent Young Scholars Program in 2015.

Jie Chen is a professor at School of Automation, Beijing Institute of Technology, China. His research interest covers complex system multi-objective optimization and decision, constrained nonlinear control, and optimization methods.

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Sun, J., Chen, J. A survey on Lyapunov-based methods for stability of linear time-delay systems. Front. Comput. Sci. 11, 555–567 (2017). https://doi.org/10.1007/s11704-016-6120-3

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