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Pinning Synchronization of Stochastic T-S Fuzzy Delayed Complex Dynamical Networks with Heterogeneous Impulsive Delays

Abstract

In this paper, we deal with the exponential pinning synchronization (PS) of stochastic T-S fuzzy delayed complex dynamical networks (FDCDNs) with heterogeneous impulsive delays. Unlike the existing works, a fuzzy memory pinning impulsive control (FMPIC) approach is proposed. In order to conquer the difficulties of studying such general system, sufficient conditions that depend on the discrete-delay and distributed-delay impulsive effects are obtained by employing the Lyapunov function, inequality techniques and stochastic analysis theory. It is shown that the PS of FDCDNs can be achieved under the designed FMPIC. Numerical simulation on basis of BA scale-free coupled network is used to illustrate the effectiveness of the theoretical results.

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Correspondence to Xin Wang.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Euntai Kim. This research was supported in part by the National Natural Science Foundation of China (Grant. 61903310 and Grant. 61771004), and in part by the Fundamental Research Funds for the Central Universities (Grant. SWU119025 and Grant. SWU119023).

Huilan Yang received her Ph.D. degree in mathematics from the School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China, in 2018. She joined the School of Mathematics and Statistics, Southwest University, Chongqing, China, in 2019. Her current research interests include T-S fuzzy systems, neural networks and complex dynamical networks.

Lan Shu received her B.A. (in applied mathematics) and M.S. degrees (in Communication and System) from the University of Electronic Science and Technology of China (UESTC), in 1984 and 1987, respectively. In 2004, she studied in University of Victoria of Australia. Currently, she is a Professor of School of Mathematical Sciences, UESTC, Chengdu, China. She is the author or co-author of more than 100 journal papers, one book, including 30 papers collected by SCI, EI, and ISTP. Her current interests involve fuzzy mathematics theory and application, rough set theory and application, and automata theory and application.

Shouming Zhong received his B.S. degree in Applied Mathematics on differential equation from University of Electronic Science and Technology of China, Chengdu, China, in 1982. He has been a Professor with the School of Mathematical Sciences, University of Electronic Science and Technology of China, since 1997. His research interests include stability theorem and its application research of the differential system, robustness control, neural network and biomathematics.

Tao Zhan received her Ph.D. degree in School of Mathematics, Shandong University, Jinan, China, in 2019. From 2017 to 2018, she was an exchange Ph.D. student in Department of Applied Mathematics, University of Waterloo, Canada. She is currently a Lecturer in School of Mathematics and Statistics, Southwest University, Chongqing, China. Her research interests include nonlinear fractional order systems, singular system, impulsive control, and stability analysis.

Xin Wang received his Ph.D. degree in software engineering from the School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China, in 2018. He joined the College of Electronic and Information Engineering, Southwest University, Chongqing, in 2019. His current research interests include hybrid systems and control, T-S fuzzy systems, synchronization of complex networks and their various applications.

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Yang, H., Shu, L., Zhong, S. et al. Pinning Synchronization of Stochastic T-S Fuzzy Delayed Complex Dynamical Networks with Heterogeneous Impulsive Delays. Int. J. Control Autom. Syst. 18, 2599–2608 (2020). https://doi.org/10.1007/s12555-019-0808-8

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Keywords

  • Complex dynamical networks
  • heterogeneous impulsive delays
  • pinning synchronization
  • T-S fuzzy system