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Improved Stability Criteria for Neural Networks with Two Additive Time-Varying Delay Components

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Abstract

In this paper, the stability analysis of neural networks with two additive time-varying delay components is considered. By constructing an augmented Lyapunov–Krasovskii functional, an improved delay-dependent stability criteria are derived by utilizing the delay-partitioning approach, which can effectively deal with the integral terms. As a result, no bounding technique is involved. Two illustrative examples are listed to show the effectiveness of the proposed method.

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References

  1. S. Arik, An analysis of global asymptotic stability of delayed neural networks. IEEE Trans. Neural Netw. 13(5), 1239–1242 (2002)

    Article  Google Scholar 

  2. J. Cao, J. Wang, Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 52(5), 920–931 (2005)

    Article  MathSciNet  Google Scholar 

  3. J. Cao, J. Lu, Synchronization of coupled neural networks with or without time-varying delays. Chaos 16(1), 013133 (2006)

    Article  MathSciNet  Google Scholar 

  4. T. Chen, X. Liu, W. Lu, Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(6), 1317–1326 (2007)

    Article  MathSciNet  Google Scholar 

  5. M. Forti, A. Tesi, New conditions for global stability of neural networks with applications to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42(7), 354–366 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. He, G.P. Liu, D. Rees, New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans. Neural Netw. 18(1), 310–314 (2007)

    Article  MathSciNet  Google Scholar 

  7. C.-H. Hua, X. Yang, J. Yan, X.-P. Guan, New exponential stability criteria for neural networks with time-varying delay. IEEE Trans. Circuits Syst. II, Express Briefs 58(12), 931–935 (2011)

    Article  Google Scholar 

  8. T. Li, L. Guo, C. Lin, Stability criteria with less LMI variables for neural networks with time-varying delay. IEEE Trans. Circuits Syst. II, Express Briefs 55(11), 1188–1192 (2008)

    Article  Google Scholar 

  9. H. Li, H. Gao, P. Shi, New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans. Neural Netw. 21(11), 1842–1847 (2011)

    Google Scholar 

  10. J. Lu, D.W.C. Ho, Z. Wang, Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers. IEEE Trans. Neural Netw. 20(10), 1617–1629 (2009)

    Article  Google Scholar 

  11. J. Lu, D.W.C. Ho, J. Cao, J. Kurths, Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans. Neural Netw. 22(2), 329–336 (2011)

    Article  Google Scholar 

  12. W. Lu, T. Chen, Synchronization of coupled connected neural networks with delays. IEEE Trans. Circuits Syst. I, Regul. Pap. 51(12), 2491–2503 (2004)

    Article  MathSciNet  Google Scholar 

  13. H. Shao, Delay-dependent approaches to globally exponential stability for recurrent neural networks. IEEE Trans. Circuits Syst. II 55(6), 591–595 (2008)

    Article  Google Scholar 

  14. H. Shao, Q. Han, New delay-dependent stability criteria for neural networks with two additive time-varying delay components. IEEE Trans. Neural Netw. 22(5), 812–818 (2011)

    Article  MathSciNet  Google Scholar 

  15. V. Singh, A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Netw. 15(1), 223–225 (2004)

    Article  Google Scholar 

  16. J. Tian, S. Zhong, Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components. Neurocomputing 77(1), 114–119 (2012)

    Article  Google Scholar 

  17. S. Xu, J. Lam, D.W.C. Ho, Y. Zou, Novel global asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Circuits Syst. II, Express Briefs 52(6), 349–353 (2005)

    Article  Google Scholar 

  18. S. Yoshizwa, M. Morita, S.I. Amari, Capacity of associative memory using a nonmonontonic neural model. Neural Netw. 6(2), 167–176 (1993)

    Article  Google Scholar 

  19. H.-B. Zeng, Y. He, M. Wu, C.-F. Zhang, Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays. IEEE Trans. Neural Netw. 22(5), 806–812 (2011)

    Article  Google Scholar 

  20. Y. Zhao, H. Gao, S. Mou, Asymptotic stability analysis of neural networks with successive time delay components. Neurocomputing 71(13–15), 2848–2856 (2008)

    Article  Google Scholar 

  21. B. Zhang, S. Xu, G. Zong, Y. Zou, Delay-dependent exponential stability for uncertain stochastic Hopfield neural networks with time-varying delays. IEEE Trans. Circuits Syst. I, Regul. Pap. 56(6), 1241–1247 (2006)

    MathSciNet  Google Scholar 

  22. H. Zhang, Z. Wang, D. Liu, Robust exponential stability of recurrent neural networks with multiple time-varying delays. IEEE Trans. Circuits Syst. II 54(8), 730–734 (2007)

    Article  Google Scholar 

  23. X.-M. Zhang, Q.-L. Han, Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans. Neural Netw. 22(8), 1180–1192 (2011)

    Article  Google Scholar 

  24. X. Zhu, G. Yang, New delay-dependent stability results for neural networks with time-varying delay. IEEE Trans. Neural Netw. 19(10), 1783–1791 (2008)

    Article  MathSciNet  Google Scholar 

  25. Y. Zhang, D. Yue, E. Tian, New stability criteria of neural networks with interval time-varying delay: a piecewise delay method. Appl. Math. Comput. 208(1), 249–259 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundations of China under Grant No. 11126278 and No. 61104027, and the Natural Science Foundation of Jiangxi Province in China under Grant No. 20114BAB211001.

The author would like to express his sincere appreciation to the Associate Editor and the anonymous reviewers for their helpful comments and valuable suggestions.

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  1. Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, P.R. China

    Huabin Chen

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  1. Huabin Chen
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Correspondence to Huabin Chen.

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Chen, H. Improved Stability Criteria for Neural Networks with Two Additive Time-Varying Delay Components. Circuits Syst Signal Process 32, 1977–1990 (2013). https://doi.org/10.1007/s00034-013-9555-x

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