Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

Xian-Ming Zhang; Qing-Long Han; Xiaohua Ge

doi:10.1109/JAS.2020.1003111

Volume 8 Issue 1

Jan. 2021

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

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X.-M. Zhang, Q.-L. Han, and X. H. Ge, "Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 77-85, . 2021. doi: 10.1109/JAS.2020.1003111

Citation:

X.-M. Zhang, Q.-L. Han, and X. H. Ge, "Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 77-85, . 2021. doi: 10.1109/JAS.2020.1003111

Citation:

X.-M. Zhang, Q.-L. Han, and X. H. Ge, "Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 77-85, . 2021. doi: 10.1109/JAS.2020.1003111

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Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

doi: 10.1109/JAS.2020.1003111

Funds: This work was supported in part by the Australian Research Council Discovery Project (Grant No. DP160103567)

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Author Bio:
Xian-Ming Zhang (M’16–SM’18) received the M.Sc. degree in applied mathematics and the Ph.D. degree in control theory and engineering from Central South University, Changsha, China, in 1992 and 2006, respectively.In 1992, he joined Central South University, where he was an Associate Professor with the School of Mathematics and Statistics. From 2007 to 2014, he was a Post-Doctoral Research Fellow and a Lecturer with the School of Engineering and Technology, Central Queensland University, Rockhampton, QLD, Australia. From 2014 to 2016, he was a Lecturer with the Griffith School of Engineering, Griffith University, Gold Coast, QLD, Australia. In 2016, he joined the Swinburne University of Technology, Melbourne, VIC, Australia, where he is currently an Associate Professor with the School of Software and Electrical Engineering. His current research interests include H-infinity filtering, event-triggered control systems, networked control systems, neural networks, distributed systems, and time-delay systems.Dr. Zhang was a recipient of second National Natural Science Award in China in 2013, and first Hunan Provincial Natural Science Award in Hunan Province in China in 2011, both jointly with Prof. M. Wu and Prof. Y. He, and the IET Premium Award in 2016, jointly with Prof. Q.-L. Han. He is an Associate Editor of the IEEE Transactions on Cybernetics, Neural Processing Letters, Journal of the Franklin Institute, International Journal of Control, Automation, and Systems and the Neurocomputing, and he is an Editorial Board Member of Neural Computing and Applications

Qing-Long Han (M’09–SM’13–F’19) received the B.Sc. degree in Mathematics from Shandong Normal University, Jinan, China, in 1983, and the M.Sc. and Ph.D. degrees in Control Engineering and Electrical Engineering from East China University of Science and Technology, Shanghai, China, in 1992 and 1997, respectively.From September 1997 to December 1998, he was a Post-doctoral Researcher Fellow with the Laboratoire d’Automatique et d’Informatique Industielle (currently, Laboratoire d’Informatique et d’Automatique pour les Systémes), École Supérieure d’Ing’enieurs de Poitiers (currently, École Nationale Supérieure d’Ingénieurs de Poitiers), Université de Poitiers, France. From January 1999 to August 2001, he was a Research Assistant Professor with the Department of Mechanical and Industrial Engineering at Southern Illinois University at Edwardsville, USA. From September 2001 to December 2014, he was Laureate Professor, an Associate Dean (Research and Innovation) with the Higher Education Division, and the Founding Director of the Centre for Intelligent and Networked Systems at Central Queensland University, Australia. From December 2014 to May 2016, he was Deputy Dean (Research), with the Griffith Sciences, and a Professor with the Griffith School of Engineering, Griffith University, Australia. In May 2016, he joined Swinburne University of Technology, Australia, where he is currently Pro Vice-Chancellor (Research Quality) and a Distinguished Professor. His research interests include networked control systems, multi-agent systems, time-delay systems, complex dynamical systems and neural networks.Professor Han is a Highly Cited Researcher according to Clarivate Analytics (formerly Thomson Reuters). He is a Fellow of The Institution of Engineers Australia. He is an Associate Editor of several international journals, including the IEEE Transactions on Cybernetics, the IEEE Transactions on Industrial Electronics, the IEEE Transactions on Industrial Informatics, IEEE Industrial Electronics Magazine, the IEEE/CAA Journal of Automatica Sinica, Control Engineering Practice, and Information Sciences

Xiaohua Ge (M'18) received the B.Eng. degree in electronics and information engineering from Nanchang Hangkong University, Nanchang, China, in 2008, the M.Eng. degree in control theory and control engineering from Hangzhou Dianzi University, Hangzhou, China, in 2011, and the Ph.D. degree in computer engineering from Central Queensland University, Rockhampton, QLD, Australia, in 2014.From 2011 to 2013, he was a Research Assistant with the Centre for Intelligent and Networked Systems, Central Queensland University, Rockhampton, QLD, Australia, where he was a Research Fellow in 2014. From 2015 to 2017, he was a Research Fellow with the Griffith School of Engineering, Griffith University, Gold Coast, QLD, Australia. He is currently a Senior Lecturer with the School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, VIC, Australia.His research interests include distributed estimation over sensor networks, distributed coordination in multi-agent systems, security and privacy preserving in cyber-physical systems
Corresponding author: The authors are with the School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, VIC 3122, Australia (e-mail: xianmingzhang@swin.edu.au; qhan@swin.edu.au; xge@swin.edu.au)
Received Date: 2020-01-02
Revised Date: 2020-02-12
Accepted Date: 2020-03-02

Available Online: 2020-03-11

Abstract

Abstract

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay. The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval. The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer. The second contribution of this paper is to introduce a novel Lyapunov-Krasovskii functional, which includes a cubic polynomial on a time-varying delay, in stability analysis of time-delay systems. Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities, two stability criteria are derived for two cases of the time-varying delay. A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.
- Bessel-Legendre inequality,
- matrix-valued polynomial inequalities,
- stability,
- time-varying delay,
- time-delay systems

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References

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Establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval;
Introduce a novel Lyapunov-Krasovskii functional;
The proposed stability criteria are of less conservativeness than some existing ones

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

doi: 10.1109/JAS.2020.1003111

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通讯作者: 陈斌, bchen63@163.com

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