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H∞ Synchronization of Uncertain Chaotic Lur’e Systems with Time-varying Delay via Stochastic Sampling

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  • Control Theory and Applications
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Abstract

In this article, the problem of H∞ synchronization for uncertain chaotic systems with time-varying delay controlled by random sampling is considered. The variable sampling period is assumed to switch stochastically between different values with given probability. In addition, the disturbance and the parameter uncertainty that may occur in many actual system are taken into account. With the help of input delay method, the chaotic Lur’e systems (CLSs) with probability sampling is converted to a continuous system. Then, based on the Lyapunov-Krasovskii functional (LKF) theory, a novel LKF is proposed. By using the reciprocal convex method, sufficient conditions are obtained to guarantee the stability of the error system and to reduce the influence of external disturbances under the condition of bounded H∞ norm. By solving a series of linear matrix inequalities (LMIs) which are obtained, the corresponding sampled data controller can be obtained. Finally, a numerical example is used to illustrate the superiority and effectiveness of proposed method.

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Funding

This work is partially supported by the Hebei Natural Science Foundation-Steel and Iron Foundation Fund (E2019105123), the Hebei Education Department Foundation Fund (ZD2019311).

Author information

Authors and Affiliations

  1. Institute of Artificial intelligence, North China University of Science and Technology, Tangshan, 063009, China

    Hanxiao Zhao & Wei Li

  2. Institute of Mining Engineering, North China University of Science and Technology, Tangshan, 063009, China

    Jiayong Zhang

  3. Institute of Electrical Engineering, North China University of Science and Technology, Tangshan, 063009, China

    Chao Ge

  4. School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China

    Yajuan Liu

Authors
  1. Hanxiao Zhao
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  2. Jiayong Zhang
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  3. Wei Li
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  4. Chao Ge
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Corresponding authors

Correspondence to Jiayong Zhang, Wei Li or Chao Ge.

Additional information

Hanxiao Zhao received her B.S. degree in internet of things engineering from Tangshan College, Tangshan, China, in 2018. She is currently pursing an M.S. degree in computer science and technology, North China University of Science and Technology, Tangshan, China. Her current research interests include sampled-data control, and chaotic Lur’e system.

Jiayong Zhang received his Ph.D. degree in mining engineering from China University of Mining and Technology, Xuzhou, China, in 2014. He is a full professor with the institution of mining engineering, North China University of Science and Technology, Tangshan, China. His current research interests include consensus problem in multi-agent systems and stability analysis for systems with time-delay.

Wei Li received his M.S. degree in computer applications technology from North China University of Science and Technology, Tangshan, China, in 2010. Currently, he is an associate professor at the College of Artificial Intelligence, North China University of Science and Technology, Tangshan, China. His research interests include robust control and intelligent control.

Chao Ge received his Ph.D. degree in electrical engineering from Yanshan University, Qinhuangdao, China, in 2015. He is currently a Full Professor with the North China University of Science and Technology, Tangshan, China. His research interests include time-delay systems, neural networks, fuzzy systems, and networked control systems.

Yajuan Liu received her B.S. degree in mathematics and applied mathematics from Shanxi Normal University, Linfen, China, in 2010, an M.S. degree in applied mathematics from the University of Science and Technology Beijing, Beijing, China, in 2012, and a Ph.D. degree from the Division of Electronic Engineering, Daegu University, Daegu, Korea, in 2015. From 2015 to 2018, she was a Post-Doctoral Research Fellow at the Department of Electrical Engineering, Yeungnam University, Gyeongsan, Korea. She is currently working as an Associate Professor with the School of Control and Computer Engineering, North China Electric Power University, Beijing. Her research interest focuses on control of dynamic systems including neural networks and complex systems.

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Zhao, H., Zhang, J., Li, W. et al. H∞ Synchronization of Uncertain Chaotic Lur’e Systems with Time-varying Delay via Stochastic Sampling. Int. J. Control Autom. Syst. 20, 1111–1121 (2022). https://doi.org/10.1007/s12555-020-0601-8

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  • DOI: https://doi.org/10.1007/s12555-020-0601-8

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