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LMI Based Global Asymptotic Stability Criterion for Recurrent Neural Networks with Infinite Distributed Delays

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Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

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Abstract

Global asymptotic stability problem for a class of recurrent neural networks with infinite distributed delay is investigated based on the linear matrix inequality (LMI) technique. Using a matrix decomposition method, a vector-matrix form of recurrent neural networks with infinite distributed delay is obtained. Then by constructing a suitable Lyapunov functional and using an inequality, new LMI-based criteria are established to ensure the global asymptotic stability of the class of neural networks, which considers the effects of neuron’s excitatory and inhibitory action in the term of infinite delay on the networks. The obtained results are independent of the size of delay and are easily verified. Numerical example shows the effectiveness of the obtained results.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 60534010, 60572070, 60728307, 60774048, 60774093), the Program for Cheung Kong Scholars and Innovative Research Groups of China (Grant No. 60521003) and the National High Technology Research and Development Program of China (Grant No. 2006AA04Z183–B08015), the Natural Science Foundation of Liaoning Province (Grant No. 20072025), the Postdoctoral Science Foundation of China ( Grant No. 20080431150) and the Postdoctoral Foundation of Northeastern University (Grant No. 20080314).

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110004, People’s Republic of China

    Zhanshan Wang, Huaguang Zhang & Jian Feng

  2. Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL60607, USA

    Derong Liu

Authors
  1. Zhanshan Wang
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  2. Huaguang Zhang
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  3. Derong Liu
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  4. Jian Feng
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Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Wang, Z., Zhang, H., Liu, D., Feng, J. (2009). LMI Based Global Asymptotic Stability Criterion for Recurrent Neural Networks with Infinite Distributed Delays. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_54

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  • DOI: https://doi.org/10.1007/978-3-642-01507-6_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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