Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

Jidong Wang; Zhanshan Wang; Sanbo Ding; Huaguang Zhang

doi:10.1109/JAS.2018.7511087

Volume 5 Issue 3

May 2018

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2018 > 5(3): 758-764

Jidong Wang, Zhanshan Wang, Sanbo Ding and Huaguang Zhang, "Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 758-764, Mar. 2018. doi: 10.1109/JAS.2018.7511087

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Jidong Wang, Zhanshan Wang, Sanbo Ding and Huaguang Zhang, "Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 758-764, Mar. 2018. doi: 10.1109/JAS.2018.7511087

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Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

doi: 10.1109/JAS.2018.7511087

Jidong Wang^{1, 2, 3
,},
Zhanshan Wang^{1, 2
,
,},
Sanbo Ding^{1, 2
,},
Huaguang Zhang^{1, 2
,}

1.
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
2.
State Key Laboratory of Synthetical Automation for Process Industries, Shenyang 110819, China
3.
College of Electrical Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Funds:

the National Natural Science Foundation of China 61473070

the National Natural Science Foundation of China 61433004

the National Natural Science Foundation of China 61627809

SAPI Fundamental Research Funds 2013ZCX01

SAPI Fundamental Research Funds 2013ZCX14

More Information

Author Bio:
Jidong Wang received the M.S. degree in control theory and control engineering from Zhejiang University of Technology in 2005.
He is currently pursuing the Ph.D. degree at the College of Information Science and Engineering, Northeastern University, and is working as an Associate Professor at the College of Electrical Engineering, North China University of Water Resources and Electric Power. His research interests include nonlinear control theory, distributed control systems, and artificial neural networks. (e-mail: kfwjd@ncwu.edu.cn)

Zhanshan Wang (M'09-SM'17) received the M.S. degree in control theory and control engineering from Liaoning Shihua University, Fushun, China, in 2001, and the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2006.
He has been a Professor with Northeastern University since 2010. He has authored or co-authored over 100 journal and conference papers and five monographs. He holds ten patents. His current research interests include the stability analysis of recurrent neural networks, fault diagnosis, fault tolerant control, nonlinear control theory, and their applications in smart grid.
Dr. Wang was an Associate Editor of IEEE Transactions on Neural Networks and Learning Systems. He is an Associate Editor of Acta Automatica Sinica. (e-mail: zhanshan_wang@163.com)

Sanbo Ding received the M.S. degree from Department of Mathematics, Yanshan University, Qinhuangdao, China, in 2014. He is currently pursuing the Ph.D. degree with the College of Information Science and Engineering, Northeastern University, Shenyang, China.
His current research interests include stability of neural networks, discontinuous dynamical systems, design and analysis of memristor-based circuits and systems, and intelligent adaptive control. (e-mail: dingsanbo@163.com)

Huaguang Zhang (SM'04-F'14) received the B.S. and M.S. degrees in control engineering from the Northeast Dianli University of China, Jilin City, China, in 1982 and 1985, respectively, and the Ph.D. degree in thermal power engineering and automation from Southeast University, Nanjing, China, in 1991.
He joined the Department of Automatic Control, Northeastern University, Shenyang, China, in 1992, as a Post-Doctoral Fellow, for two years. Since 1994, he has been a Professor and the head of the Institute of Electric Automation with the School of Information Science and Engineering, Northeastern University. His current research interests include neural networks-based control, fuzzy control, stochastic system control, nonlinear control, and their applications. He has authored or co-authored over 200 journal and conference papers, six monographs, and holds 20 patents.
Dr. Zhang is an Associate Editor of Automatica, IEEE Transactions on Cybernetics, and Neurocomputing. He received the Outstanding Youth Science Foundation Award from the National Natural Science Foundation Committee of China in 2003. He was named the Cheung Kong Scholar by the Education Ministry of China in 2005. (e-mail: zhanghuaguang@mail.neu.edu.cn)
Corresponding author: Zhanshan Wang, e-mail: zhanshan_wang@163.com
Received Date: 2017-10-24
Accepted Date: 2018-01-09

Abstract

Abstract

This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional (LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.
- Multiple integral approach,
- refined Jensenbased multiple integral inequality (RJMII),
- stability analysis,
- time-delay systems

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References(34)

References

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Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

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