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New stability criteria for recurrent neural networks with a time-varying delay

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Abstract

This paper deals with the stability of static recurrent neural networks (RNNs) with a time-varying delay. An augmented Lyapunov-Krasovskii functional is employed, in which some useful terms are included. Furthermore, the relationship among the time-varying delay, its upper bound and their difference, is taken into account, and novel bounding techniques for 1 − \( \dot \tau \) (t) are employed. As a result, without ignoring any useful term in the derivative of the Lyapunov-Krasovskii functional, the resulting delay-dependent criteria show less conservative than the existing ones. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, 412008, PRC

    Hong-Bing Zeng, Shen-Ping Xiao & Bin Liu

  2. School of Information Science and Engineering, Central South University, Changsha, 410083, PRC

    Hong-Bing Zeng

  3. School of Engineering, Australian National University, Canberra, ACT, 0200, Australia

    Bin Liu

Authors
  1. Hong-Bing Zeng
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  2. Shen-Ping Xiao
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  3. Bin Liu
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Corresponding author

Correspondence to Hong-Bing Zeng.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60874025) and Natural Science Foundation of Hunan Province of China (No. 10JJ6098).

Hong-Bing Zeng received the B. Sc. degree in electrical engineering from Tianjin University of Technology and Education, Tianjin, PRC in 2003, and M. Sc. degree in computer science from Central South University of Forestry, Changsha, PRC in 2006. He is currently a Ph. D. candidate in control science and engineering from Central South University. Since July 2003, he has been with the School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, PRC, where he became a lecturer in 2008.

His research interests include time-delay systems and networked control systems.

Shen-Ping Xiao received the B. Sc. degree in engineering from Northeastern University, Shenyang, PRC in 1988, and Ph.D. degree in control science and engineering from Central South University, Changsha, PRC in 2008. Currently, he is a professor in the School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, PRC.

His research interests include robust control and its applications, intelligent control, and process control.

Bin Liu received the M. Sc. degree from the Department of Mathematics, East China Normal University, Shanghai, PRC in 1993, and Ph.D. degree from the Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, PRC in June 2003. He was a postdoctoral fellow at the Huazhong University of Science and Technology from July 2003 to July 2005, a postdoctoral fellow at the University of Alberta, Edmonton, AB, Canada from August 2005 to October 2006, and a visiting research fellow at the Hong Kong Polytechnic University, Hong Kong, PRC in 2004. Since July 1993, he has been with the School of Information and Computation Science and School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, PRC, where he became an associate professor in 2001, and a professor in 2004. Now, he is a research fellow in the School of Engineering, the Australian National University, ACT, Australia.

His research interests include stability analysis and applications of nonlinear systems and hybrid systems, optimal control and stability, chaos and network synchronization and control and Lie algebra.

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Zeng, HB., Xiao, SP. & Liu, B. New stability criteria for recurrent neural networks with a time-varying delay. Int. J. Autom. Comput. 8, 128–133 (2011). https://doi.org/10.1007/s11633-010-0564-y

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  • DOI: https://doi.org/10.1007/s11633-010-0564-y

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