Exponential Synchronization Control of Neural Networks with Time-Delays and Markovian Jumping Parameters

  • Yuqing Sun
  • Yiyuan Zheng
  • Xiangwu Ding
  • Yiming Gan
  • Wuneng ZhouEmail author
  • Xin Zhang
  • Lifei Yang
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 528)


In this paper, the exponential synchronization control is considered for neural networks with time-delays and Markovian jumping parameters. The jumping parameters are modeled as continuous-time finite-state Markov chain. By resorting to the Lyapunov functional method, a linear matrix inequality (LMI) approach is developed to derive the synchronization required. Simulations with Matlab verify the effectiveness of the proposes criteria.


Exponential synchronization Markovian jumping Time-delays Linear matrix inequality 


  1. 1.
    S. Arik, Stability analysis of delayed neural networks. IEEE Trans Circuits Syst-I 47, 1089–1092 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Z. Wu, H. Su, J. Chu, W. Zhou, Improved result on stability analysis of discrete stochastic neural networks with time delay. Phys. Lett. A 373(17), 1546–1552 (2009)Google Scholar
  3. 3.
    Z. Wu, P. Shi, H. Su, J. Chu, Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled-data. IEEE Trans. Cybern. 43(6), 1796–1806 (2013)Google Scholar
  4. 4.
    W. Zhou, D. Tong, Y. Gao, C. Ji, H. Su, Mode and delay-dependent adaptive exponential synchronization in pth moment for stochastic delayed neural networks with Markovian switching. IEEE Trans. Neural Netw. Learn. Syst. 23(4), 662–668 (2012)Google Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Y. Sun, W. Zhou, Exponential stability of stochastic neural networks with time-variant mixed time-delays and uncertainty, in 9th IEEE Conference on Industrial Electronics and Applications (ICIEA) (2014)Google Scholar
  7. 7.
    Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4–6), 299–308 (2005)Google Scholar
  8. 8.
    S. Ma, W. Zhou, S. Luo, R. Chen, Projective synchronization control of delayed recurrent neural networks with Markovian jumping parameters, in 8th International Conference on Computational Intelligence and Security (2012)Google Scholar
  9. 9.
    W. Zhou, Q. Zhu, P. Shi, H. Su, J. Fang, L. Zhou, Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters. IEEE Trans. Cybern. 44(12), 2848–2860 (2014)CrossRefGoogle Scholar
  10. 10.
    Z. Wu, P. Shi, H. Su, J. Chu, Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans. Neural Netw. Learn. Syst. 23(9), 1368–1376 (2012)Google Scholar
  11. 11.
    Z. Wu, P. Shi, H. Su, H. Chu, Delay-dependent stability analysis for switched neural networks with time-varying delay. IEEE Trans. Syst. Man Cybern. B Cybern. 41(6), 1522–1530 (2011)Google Scholar
  12. 12.
    Z. Wang, S. Lauria, J. Fang, Y. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos, Solitons Fractals 32, 62–72 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Y. Liu, Z. Wang, X. Liu, Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19(5), 667–675 (2006)CrossRefGoogle Scholar
  14. 14.
    Y. Wang, L. Xie, C.E. de Souza, Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19, 139–149 (1992)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Y. Jia, Robust control with decoupling performance for steering and traction of 4WS vehicles under velocity-varying motion. IEEE Trans. Control Syst. Technol. 8(3), 554–569 (2000)CrossRefGoogle Scholar
  16. 16.
    Y. Jia, Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predictive approach. IEEE Trans. Autom. Control 48(8), 1413–1416 (2003)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yuqing Sun
    • 1
  • Yiyuan Zheng
    • 2
  • Xiangwu Ding
    • 1
  • Yiming Gan
    • 3
  • Wuneng Zhou
    • 1
    Email author
  • Xin Zhang
    • 1
  • Lifei Yang
    • 4
  1. 1.College of Information Science and TechnologyDonghua UniversityShanghaiChina
  2. 2.Wenlan School of BusinessZhongnan University of Economics and LawWuhanChina
  3. 3.Bros Eastern Stock Co., LtdNingboChina
  4. 4.Glorious Sun School of Business and ManagementDonghua UniversityShanghaiChina

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