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Improved Synchronization Analysis for Delayed Lur’e Systems Using Improved Technique

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Abstract

The master-slave synchronization (MSS) issue of chaotic Lur’e systems (LSs) with time-varying delay (TVD) is explored in this work by means of feedback control. After taking the nonlinear function into full consideration, a creative Lyapunov-Krasovskii functional (LKF) is attained. Then novel criteria which ensure the synchronization of the studied systems are obtained with the aid of the improved inequality technique and the reciprocally convex combination method to cope with the derivative of LKF. The effectiveness and virtues of the synchronization conditions are testified via the notable Chua’s circuit in three different cases.

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Correspondence to Lianglin Xiong.

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Recommended by Associate Editor Yajuan Liu under the direction of Editor Jessie (Ju H.) Park.

The authors thank the editors and the reviewers for their valuable comments of this paper.

This work was supported by the National Natural Science Foundation of China under Grant No.12061088.

Yefan Wu received her B.Sc. degree in mathematics and applied mathematics from Huaibei Normal University, Huaibei, China, in 2006. She received her M.Sc. in basic mathematics from Yunnan Minzu University, Yunnan, China, in 2020. Her research interests include nonlinear control and neutral dynamical systems.

Lianglin Xiong obtained his bachelor’s degree in mathematics and applied mathematics from Neijiang Normal University, Sichuan, China, in 2004. He got his Master and Doctoral degrees in applied mathematics from University of Electronic Science and Technology of China, Sichuan, China, in 2007 and 2009, respectively. He is a professor of the School of Mathematics and Computer Science, Yunnan Minzu University. He has reviewed for many journals, such as Journal of Computational and Applied Mathematics, Automatica, Journal of the Franklin Institute, International Journal of Systems Science, Neurocomputing, International Journal of Control, Automation, and Systems and so on. His research interests include stability analysis and controller design for functional differential systems such as neutral delayed systems, neural networks, Lur’e systems, switched systems, and Markovian jump systems.

Guisheng Zhai received his B.S. degree from Fudan University, China, in 1988, and received his M.E. and Ph.D. degrees, both in system science, from Kobe University, Japan, in 1993 and 1996, respectively. After two years of industrial experience, Dr. Zhai moved to Wakayama University, Japan, in 1998, and then to Osaka Prefecture University, Japan, in 2004. He held visiting professor positions at University of Notre Dame, Purdue University, Taiyuan University of Technology, Hubei University of Technology, and Fujian Normal University, etc. In April 2010, he joined Shibaura Institute of Technology, Japan, where he currently is a full Professor of Mathematical Sciences. His research interests include large scale and decentralized control systems, robust control, switched systems and switching control, networked control and multi-agent systems, neural networks and signal processing, etc. Dr. Zhai is on the editorial board of several academic journals including IET Control Theory and Applications, International Journal of Applied Mathematics and Computer Science, Journal of Control and Decision, Frontiers of Mechanical Engineering, Science Nature, Data Analytics and Applied Mathematics, etc. He is a Senior Member of IEEE, a member of ISCIE, SICE, JSST and JSME.

Tao Wu received his B.Sc. degree in mathematics and applied mathematics from Yunnan Minzu University, Yunnan, China, in 2016. He received his M.Sc. degree in basic mathematics from Yunnan Minzu University, Yunnan, China, in 2019. His research interests include nonlinear control, neutral dynamical systems, and complex networks.

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Wu, Y., Xiong, L., Zhai, G. et al. Improved Synchronization Analysis for Delayed Lur’e Systems Using Improved Technique. Int. J. Control Autom. Syst. 19, 1480–1490 (2021). https://doi.org/10.1007/s12555-020-0111-8

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