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Enhanced Global Asymptotic Stabilization Criteria for Delayed Fractional Complex-valued Neural Networks with Parameter Uncertainty

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  • Control Theory and Applications
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Abstract

This paper addresses the global asymptotic stabilization of delayed fractional complex-valued neural networks (FCVNNs) subject to bounded parameter uncertainty. The problem is proposed for two reasons: 1) The available methods for uncertain dynamical systems may be too conservative; 2) The existing algebraic conditions will lead to huge computational burden for large-scale FCVNNs. To surmount these difficulties, the delayed FCVNNs with interval parameters are transformed into a tractable form at first. Then, a simple and practical controller–linear state feedback controller is designed to achieve the global asymptotic stabilization. By constructing different Lyapunov functions and utilizing the fractional-order comparison principle and interval matrix method, two sufficient global asymptotic stabilization criteria expressed in LMI forms, are established. The obtained results in this paper improve and extend some previous published results on FCVNNs. Finally, two numerical examples are provided to illustrate the correctness of the theoretical results.

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Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Xiaohong Wang & Yingjie Fan

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhen Wang

  3. College of Mathematic Science, Liaocheng University, Liaocheng, 252000, China

    Jianwei Xia

  4. School of Electrical Engineering and Information, Anhui University of Technology, Anhui, 233100, China

    Hao Shen

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  1. Xiaohong Wang
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  2. Zhen Wang
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  5. Hao Shen
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Correspondence to Zhen Wang.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China (Nos. 61573008, 61473178), National Natural Science Foundation of Shandong Province under Grant (No. ZR2018MF005) and SDUST Research Fund (No. 2018TDJH101).

Xiaohong Wang received the B.E. degree in Computing and Mathematics from Shandong University of Science and Technology, Qingdao, China in 2015. She is currently pursuing a Ph.D. degree with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China. Her current research interests include neural networks, fractional order systems, sampled-data control, event-triggered control.

Zhen Wang received the B.S. degree in mathematics from Ocean University of China, Qingdao, China in 2004 and the Ph.D. degree in the School of Automation, Nanjing University of Science and Technology, Nanjing, China in 2014. He has been an Associate Professor at the College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China since 2006. His current research interest covers computational mathematics, neural networks, fractional order systems, and multi-agent systems.

Yingjie Fan received the B.S. degree from the University of Jinan, Jinan, China, in 2010. He is currently pursuing a Ph.D. degree in control theory and control engineering with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China. His current research interest include networked control, memristorbased circuits and systems, and fractional-order nonlinear systems.

Jianwei Xia received his B.Sc. degree from Liaocheng University, Shandong, China in 2001, an M.S. degree from Qufu Normal University, Shandong, China in 2004 and a Ph.D. degree from Nanjing University of Science and Technology, Nanjing, China, in 2007. From April to October in 2006, he was a Visiting Scholar in City University of Hong Kong, Hong Kong, China. From 2010 to 2012, he was a Post-Doctoral Researcher with the School of Automation, Southeast University, Nanjing, China. He joined the School of Mathematical Sciences, Liaocheng University in 2007. His current research interests include robust control and filtering, switching systems, stochastic systems and time-delay systems.

Hao Shen received the Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 2011. From February 2013 to March 2014, he was a Post-Doctoral Fellow with the Department of Electrical Engineering, Yeungnam University, Republic of Korea. Since 2011, he has been with Anhui University of Technology, China, where he is currently a Professor and a Doctoral Supervisor. His current research interests include stochastic hybrid systems, complex networks, fuzzy systems and control, nonlinear control. Dr. Shen has served on the technical program committee for several international conferences. He is an Associate Editor/Guest Editor for several international journals, including Journal of The Franklin Institute, Applied Mathematics and Computation, Transactions of the Institute Measurement and Control and Mathematical Problems in Engineering.

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Wang, X., Wang, Z., Fan, Y. et al. Enhanced Global Asymptotic Stabilization Criteria for Delayed Fractional Complex-valued Neural Networks with Parameter Uncertainty. Int. J. Control Autom. Syst. 17, 880–895 (2019). https://doi.org/10.1007/s12555-018-0679-4

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