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Novel LMI Criteria for Stability of Neural Networks with Distributed Delays

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Advances in Neural Networks – ISNN 2007 (ISNN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4491))

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Abstract

In this paper, the global asymptotic and exponential stability are investigated for a class of neural networks with distributed time-varying delays. By using appropriate Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique, two delay-dependent sufficient conditions in LMIs form are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. The proposed stability criteria do not require the monotonicity of the activation functions and the differentiability of the distributed time-varying delays, which means that the results generalize and further improve those in the earlier publications. An example is given to show the effectiveness of the obtained condition.

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References

  1. Lu, H., Chung, F.L., He, Z.: Some Sufficient Conditions for Global Exponential Stability of Hopfield Neural Networks. Neural Networks 17, 537–544 (2004)

    Article  MATH  Google Scholar 

  2. Arik, S.: An Analysis of Exponential Stability of Delayed Neural Networks with Time Varying Delays. Neural Networks 17, 1027–1031 (2004)

    Article  MATH  Google Scholar 

  3. Cao, J., Li, X.: Stability in Delayed Cohen-Grossberg Neural Networks: LMI Optimization Approach. Physica D 212, 54–65 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cao, J., Wang, J.: Global Asymptotic and Robust Stability of Recurrent Neural Networks with Time Delays. IEEE Trans. Circuits and Systems I 52, 417–426 (2005)

    Article  MathSciNet  Google Scholar 

  5. Li, C., Liao, X., Zhang, R.: A Global Exponential Robust Stability Criterion for Interval Delayed Neural Networks with Variable Delays. Neurocomputing 69, 803–809 (2006)

    Article  Google Scholar 

  6. Park, J.H.: A Novel Criterion for Global Asymptotic Stability of BAM Neural Networks with Time Delays. Chaos, Solitons and Fractals 29, 446–453 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Xu, S., Lam, J., Ho, D.W.C.: A New LMI Condition for Delay-dependent Asymptotic Stability of Delayed Hopfield Neural Networks. IEEE Transactions on Circuits and Systems II 53, 230–234 (2006)

    Article  Google Scholar 

  8. Zeng, Z., Wang, J.: Improved Conditions for Global Exponential Stability of Recurrent Neural Networks with Time-varying Delays. IEEE Transactions on Neural Networks 17, 623–635 (2006)

    Article  Google Scholar 

  9. Yang, H., Chu, T., Zhang, C.: Exponential Stability of Neural Networks with Variable Delays via LMI Approach. Chaos, Solitons and Fractals 30, 133–139 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Singh, S.: Simplified LMI Condition for Global Asymptotic Stability of Delayed Neural Networks. Chaos, Solitons and Fractals 29, 470–473 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. De, V.B., Principe, J.C.: The Gamma Model-A New Neural Model for Temporal Processing. Neural Networks 5, 565–576 (1992)

    Article  Google Scholar 

  12. Zhao, H.: Global Asymptotic Stability of Hopfield Neural Network Involving Distributed Delays. Neural Networks 17, 47–53 (2004)

    Article  MATH  Google Scholar 

  13. Liao, X., Liu, Q., Zhang, W.: Delay-dependent Asymptotic Stability for Neural Networks with Distributed Delays. Nonlinear Analysis: Real World Applications 7, 1178–1192 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, B., Huang, L.: Global Exponential Stability of BAM Neural Networks with Recent-history Distributed Delays and Impulses. Neurocomputing 69, 2090–2096 (2006)

    Article  Google Scholar 

  15. Huang, T.: Exponential Stability of Fuzzy Cellular Neural Networks with Distributed Delay. Physics Letters A 351, 48–52 (2006)

    Article  MATH  Google Scholar 

  16. Jiang, H., Teng, Z.: Boundedness and Global Stability for Nonautonomous Recurrent Neural Networks with Distributed Delays. Chaos, Solitons and Fractals 30, 83–93 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Liang, J., Cao, J.: Global Output Convergence of Recurrent Neural Networks with Distributed Delays. Nonlinear Analysis: Real World Applications 8, 187–197 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Cao, J., Yuan, K., Li, H.: Global Asymptotical Stability of Recurrent Neural Networks with Multiple Discrete Delays and Distributed Delays. IEEE Transactions on Neural Networks 17, 1646–1651 (2006)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China

    Qiankun Song

  2. College of Civil Engineering and Architecture, Chongqing Jiaotong University, Chongqing 400074, China

    Jianting Zhou

Authors
  1. Qiankun Song
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  2. Jianting Zhou
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering (M/C 154), University of Illinois at Chicago, 851 S. Morgan Street, 60607-7053, Chicago, IL, USA

    Derong Liu

  2. School of Automation, Southeast University, 210096, Nanjing, China

    Shumin Fei

  3. Laboratory of Complex Systems, Institute of Automation, Chinese Adacemy of Sciences, 100080, Beijing, P. R. China

    Zeng-Guang Hou

  4. School of Information Science and Engineering, Northeast University, Shenyang, 110004, China

    Huaguang Zhang

  5. School of Electrical Engineering, Hohai University, Nanjing, 210098, China

    Changyin Sun

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© 2007 Springer-Verlag Berlin Heidelberg

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Song, Q., Zhou, J. (2007). Novel LMI Criteria for Stability of Neural Networks with Distributed Delays. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_114

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  • DOI: https://doi.org/10.1007/978-3-540-72383-7_114

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72382-0

  • Online ISBN: 978-3-540-72383-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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