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Global Exponential Stability Analysis in Cellular Neural Networks with Time-Varying Coefficients and Delays

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Computational Intelligence and Bioinspired Systems (IWANN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3512))

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Abstract

Global exponential stability of cellular neural networks with time-varying coefficients and delays is considered in this paper. By utilizing a delay differential inequality, a new sufficient condition ensuring global exponential stability for cellular neural networks with time-varying coefficients and delays is presented. Since the condition does not require that the delay function be differentiable or the coefficients be bounded, the results here improve and extend those given in the earlier literature.

The project was supported by the National Natural Science Foundation of China (Grant No. 60403001)and China Postdoctoral Science Foundation.

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References

  1. Roska, T., Chua, L.: Cellular neural networks with delay type template elements and nonuniform grids. International Journal of Circuit Theory and Application 20, 469–481 (1992)

    Article  MATH  Google Scholar 

  2. Arik, S.: An improved global stability result for delayed cellular neural networks. IEEE Trans. Circuits Syst.I 49, 1211–1214 (2002)

    Article  MathSciNet  Google Scholar 

  3. Arik, S.: An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Networks 13, 1239–1242 (2002)

    Article  Google Scholar 

  4. Cao, J., Wang, J.: Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst.I 50, 34–44 (2003)

    Article  MathSciNet  Google Scholar 

  5. Chen, A., Cao, J., Huang, L.: An estimation of upperbound of delays for global asymptotic stability of delayed Hopfiled neural networks. IEEE Trans. Circuits Syst. I 49, 1028–1032 (2002)

    Article  MathSciNet  Google Scholar 

  6. Feng, C.H., Plamondon, R.: On the stability analysis of delayed neural networks systems. Neural Networks 14, 1181–1188 (2001)

    Article  Google Scholar 

  7. Huang, H., Cao, J.: On global asymptotic stability of recurrent neural networks with time-varying delays. Appl. Math. Comput. 142, 143–154 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Liao, X., Chen, G., Sanchez, E.N.: LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. Circuits Syst.I 49, 1033–1039 (2002)

    Article  MathSciNet  Google Scholar 

  9. Liao, X.X., Wang, J.: Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays. IEEE Trans. Circuits Syst.I 50, 268–274 (2003)

    Article  MathSciNet  Google Scholar 

  10. Mohamad, S., Gopalsamy, K.: Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl. Math. Comput. 135, 17–38 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Roska, T., Wu, C.W., Chua, L.O.: Stability of cellular neural network with dominant nonlinear and delay-type templates. IEEE Trans. Circuits Syst. 40, 270–272 (1993)

    Article  MATH  Google Scholar 

  12. Zeng, Z., Wang, J., Liao, X.: Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst.I 50, 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  13. Zhang, J.: Globally exponential stability of neural networks with variable delays. IEEE Trans. Circuits Syst.I 50, 288–290 (2003)

    Article  Google Scholar 

  14. Zhang, Q., Ma, R., Xu, J.: Stability of cellular neural networks with delay. Electron. Lett. 37, 575–576 (2001)

    Article  Google Scholar 

  15. Qiang, Z., Ma, R., Chao, W., Jin, X.: On the global stability of delayed neural networks. IEEE Trans. Automatic Control 48, 794–797 (2003)

    Article  Google Scholar 

  16. Zhang, Q., Wei, X.P., Xu, J.: Global Exponential Convergence Analysis of Delayed Neural Networks with Time-Varying Delays. Phys. Lett. A 318, 537–544 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhang, Q., Wei, X.P., Xu, J.: Global Asymptotic Stability of Hopfield Neural Networks with Transmission Delays. Phys. Lett. A 318, 399–405 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang, Q., Wei, X.P., Xu, J.: An Analysis on the Global Asymptotic Atability for Neural Networks with Variable Delays. Phys. Lett. A 328, 163–169 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhang, Q., Wei, X.P., Xu, J.: On Global Exponential Stability of Delayed Cellular Neural Networks with Time-Varying Delays. Appl. Math. Comput. 162, 679–686 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhang, Q., Wei, X.P., Xu, J.: Delay-Dependent Exponential Stability of Cellular Neural Networks with Time-Varying Delays. Chaos, Solitons & Fractals 23, 1363–1369 (2005)

    MATH  MathSciNet  Google Scholar 

  21. Zhou, D., Cao, J.: Globally exponential stability conditions for cellular neural networks with time-varying delays. Appl. Math. Comput. 131, 487–496 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  22. Jiang, H., Li, Z., Teng, Z.: Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306, 313–325 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Jiang, H., Li, Z., Teng, Z.: Boundedness and stability for nonautonomous cellular neural networks with delay. Phys. Lett. A 306, 313–325 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Liang, J., Cao, J.: Bounded and stability for recurrent neural networks with variable coefficients and time-varying delays. Phys. Lett. A 318, 53–64 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  25. Rehim, M., Jiang, H., Teng, Z.: Bounded and stability for nonautonomous cellular neural networks with delay. Neural Networks 17, 1017–1025 (2004)

    Article  MATH  Google Scholar 

  26. Chua, L.O., Yang, L.: Cellular neural networks:theory and applications. IEEE Trans. Circuits Syst.I 35, 1257–1290 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  27. Hou, C., Qian, J.: Remarks on quantitative analysis for a family of scalar delay differential inequalities. IEEE Trans. Automatic Control 44, 334–336 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University Key Lab of Information Science & Engineering, Dalian University, Dalian, 116622, China

    Qiang Zhang, Xiaopeng Wei & Jin Xu

  2. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Dongsheng Zhou

Authors
  1. Qiang Zhang
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  2. Dongsheng Zhou
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  3. Xiaopeng Wei
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  4. Jin Xu
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Editor information

Editors and Affiliations

  1. Departamento de Ingeniería Electrónica, Universitat Politècnica de Catalunya (UPC). E.T.S.I. de Telecomunicación, Campus Norte, Edificio C4, C/ Jordi Girona, 1-3, E08034, Barcelona, Spain

    Joan Cabestany

  2. Department of Computer Architecture and Computer Technology, University of Granada,  

    Alberto Prieto

  3. Grupo ISIS, Dpto. Tecnología Electrónica ETSI Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Sandoval

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© 2005 Springer-Verlag Berlin Heidelberg

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Zhang, Q., Zhou, D., Wei, X., Xu, J. (2005). Global Exponential Stability Analysis in Cellular Neural Networks with Time-Varying Coefficients and Delays. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_46

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  • DOI: https://doi.org/10.1007/11494669_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26208-4

  • Online ISBN: 978-3-540-32106-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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