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Improved Results for Exponential Stability of Neural Networks with Time-Varying Delays

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Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

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Abstract

This paper presents several exponential stability criteria for delayed neural networks with time-varying delays and a general class of activation functions, which are derived by employing Lyapyunov-Krasovskii functional approach and linear matrix inequality technique. The proposed results are shown theoretically and numerically to be less restrictive and more easily verified than those reported recently in the open literature. In addition, an approach to estimate the degree of exponential convergence is also formulated.

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References

  1. Yuce, E., Arik, S.: New Exponential Stability Results for Delayed Neural Networks with Time Varying Delays. Physica D 191, 314–322 (2004)

    Article  MathSciNet  Google Scholar 

  2. Liao, X.F., Chen, G.R., Sanchez, E.N.: Delay-Dependent Exponential Stability Analysis of Delayed Neural Networks: an LMI Approach. Neural Networks 15, 855–866 (2002)

    Article  Google Scholar 

  3. Zeng, Z., Wang, J., Liao, X.X.: Global Exponential Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE TCAS-I 50, 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  4. Liao, X.F., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE TCAS-I 50, 268–274 (2003)

    Article  MathSciNet  Google Scholar 

  5. Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequality in Systems and Control Theory. SIAM, Philadelphia (1994)

    Google Scholar 

  6. Liao, X.F., Wong, K.W., Wu, Z.: Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays. IEEE TNN 14, 222–227 (2003)

    Google Scholar 

  7. Liao, X.F., Chen, G.R., Sanchez, E.N.: LMI-based Approach for Asymptotically Stability Analysis of Delayed. Neural Networks 49, 1033–1039 (2001)

    MathSciNet  Google Scholar 

  8. Liao, X.F., Wong, K.W., Wu, Z., Chen, G.R.: Novel Robust Stability Criteria for Interval- Delayed Hopfield Neural Networks. IEEE TCAS-I 48, 1355–1359 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liao, X.F., Wong, K.W., Yu, J.: Stability Switches and Bifurcation Analysis of a Neural Network with Continuously Delay. IEEE TSMC-A 29, 692–696 (1999)

    Google Scholar 

  10. Liao, X.F., Yu, J.: Robust Stability for Interval Hopfield Neural Networks with Time Delay. IEEE TNN 9, 1042–1045 (1998)

    Google Scholar 

  11. Cao, J., Wang, L.: Exponential Stability and Periodic Oscillatory Solution in Bam Networks with Delays. IEEE TNN 13, 457–463 (2002)

    Google Scholar 

  12. Sun, C., Feng, C.: Exponential Periodicity of Continuous-time and Discrete-Time Neural Networks with Delays. Neural Processing Letters 19, 131–146 (2004)

    Article  MathSciNet  Google Scholar 

  13. Sun, C., Feng, C.: On Robust Exponential Periodicity of Interval Neural Networks with Delays. Neural Processing Letters 20, 53–61 (2004)

    Article  Google Scholar 

  14. Li, C., Liao, X., Zhang, R.: Global Robust Asymptotical Stability of Multi-delayed Interval Neural Networks: an LMI approach. Physics Letters A 328, 452–462 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Li, C., Liao, X.F.: New Algebraic Conditions for Global Exponential Stability of Delayed Recurrent Neural Networks. Neurocomputing 64C, 319–333 (2005)

    Google Scholar 

  16. Li, C., Liao, X.F.: Delay-dependent Exponential Stability Analysis of Bi-directional Associative Memory Neural Networks: an LMI Approach. Chaos, Solitons & Fractals 24, 1119–1134 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Liao, X.F., Li, C.: An LMI Approach to Asymptotical Stability of Multi-Delayed Neural Networks. Physica D 200, 139–155 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Wu, D., Xiong, Q., Li, C., Zhang, Z., Tang, H. (2005). Improved Results for Exponential Stability of Neural Networks with Time-Varying Delays. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_19

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  • DOI: https://doi.org/10.1007/11427391_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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