Exponential stability analysis of time-delay systems based on Taylor expansion-based weighted integral inequality

ABSTRACT

This paper investigates the problem of exponential stability analysis of linear time-delay systems. First, based on the Gram-Schmidt-based integral inequality and the Taylor expansion of exponential function, we develop a new weighted multiple integral inequality called Taylor expansion-based weighted integral inequality. Second, a new Lyapunov-krasovskii functional is constructed, and then, with the help of the Taylor expansion-based inequality, a new exponential stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are presented to show the effectiveness of the newly established stability criterion.

Keywords:

• Linear time-delay system
• exponential stability
• Lyapunov-Krasovskii functional
• linear matrix inequality
• Taylor expansion
• weighted integral inequality

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Guopu Zhu  http://orcid.org/0000-0001-7956-5343

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 61572489 and Grant 61872350, in part by the Youth Innovation Promotion Association of CAS under Grant 2015299, in part by the Basic Research Program of Shenzhen under Grant JCYJ20170818163403748, in part by the Shenzhen International S&T Cooperation Project under Grant GJHZ20160229194322570, and in part by the Shenzhen Discipline Construction Project for Urban Computing and Data Intelligence.

Notes on contributors

Cheng Gong

Cheng Gong received the B.S., M.S., and Ph.D. degrees from the Harbin Institute of Technology, Harbin, China, in 2002, 2004, and 2008, respectively. He is currently an Associate Professor with the School of Mathematical Science, Heilongjiang University. His research interests mainly include stability analysis and stabilisation for linear time-delay systems, H-infinity control and filtering, T-S fuzzy system with time delay, Multi-agent Systems, Markovian Jump Systems and integral inequality related to Lyapunov stability.

Guopu Zhu

Guopu Zhu received the B.S. degree from Jilin University, China, in 2002, and the M.S. and Ph.D. degrees from the Harbin Institute of Technology, China, in 2004 and 2007, respectively. He was a Postdoctoral Fellow with Sun Yat-sen University, Guangzhou, China, and a Senior Research Associate with the City University of Hong Kong, Hong Kong. Dr Zhu is currently a Professor with the Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences (CAS), China, where he is the Director of the Center for Internet of Things Computing. His main research areas are multimedia security, image processing, and control theory. He has authored or co-authored nearly 30 papers in peer-reviewed international journals. He currently serves as an Associate Editor of the Journal of Information Security and Applications. He is a member of the Youth Innovation Promotion Association, CAS, and a senior member of IEEE.

Yan Shi

Yan Shi received the B.Sc. degree in Applied Mathematics from Northeast Heavy Machinery Institute (now Yanshan University), China, 1982; the M.Sc. degree in Applied Mathematics from Dalian Maritime University, China, 1988; the Ph.D. degree in Information and Computer Sciences, from Osaka Electro-Communication University, Japan, 1997. Dr Shi is currently a professor at the Graduate School of Science and Technology, Tokai University, Japan. His research interests include approximate reasoning, fuzzy reasoning, fuzzy system modelling and applications, neuro-fuzzy learning algorithms for system identification. He has published over 200 papers in journals and conferences. He has actively served in a number of journals. He is the Executive Editor of International Journal of Innovative Computing, Information and Control; Editor-in-Chief of International Journal of Biomedical Soft Computing and Human Sciences; and Editor-in-Chief of ICIC Express Letters. He is a member, the board of directors of Biomedical Fuzzy Systems Association.