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Nonlinear Dynamics

, Volume 95, Issue 2, pp 943–955 | Cite as

Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays

  • Leimin WangEmail author
  • Ming-Feng Ge
  • Junhao Hu
  • Guodong Zhang
Original Paper
  • 193 Downloads

Abstract

This paper investigates the stability and stabilization of inertial memristive neural networks (IMNNs) with discrete and unbounded distributed delays. The considered IMNNs are described as hybrid neural systems with second-order derivatives due to the combination of memristor and inertial items. By invoking an appropriate variable substitution method, the hybrid neural system is turned into a first-order differential system. Then, based on the nonsmooth analysis and Lyapunov stability theories, several new algebraic conditions for the global stability of IMNNs with unbounded distributed delays are derived. In addition, two simple classes of feedback control laws are designed for the considered IMNNs and the corresponding stabilizability criteria are established. Finally, two numerical examples and their discussions are provided to illustrate the validity and superiority of the theoretical results.

Keywords

Stability Stabilization Inertial items Memristive neural networks Unbounded distributed delays 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61703377, 61703374, 61876192, and 61603419, and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under Grants CUG170632 and CUG170656.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Strukov, D.B., Snider, G.S., Stewart, G.R., Williams, R.S.: The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  2. 2.
    Jo, S.H., Chang, T., Ebong, I., Bhadviya, B.B., Mazumder, P., Lu, W.: Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10(4), 1297–1301 (2010)CrossRefGoogle Scholar
  3. 3.
    Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)CrossRefGoogle Scholar
  4. 4.
    Sharifi, M.J., Banadaki, Y.M.: General SPICE models for memristor and application to circuit simulation of memristor-based synapses and memory cells. J. Circuits Syst. Comput. 19, 407–424 (2010)CrossRefGoogle Scholar
  5. 5.
    Hu, J., Wang, J.: Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays. In International Joint Conference on Neural Network IJCNN, pp. 1–8 (2010)Google Scholar
  6. 6.
    Bao, H., Park, J.H., Cao, J.: Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn. 82(3), 1343–1354 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Wu, A., Zeng, Z.: Exponential stabilization of memristive neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. 23, 1919–1929 (2012)CrossRefGoogle Scholar
  8. 8.
    Wang, Z., Ding, S., Huang, Z., Zhang, H.: Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method. IEEE Trans. Neural Netw. Learn. Syst. 27, 2337–2350 (2016)CrossRefGoogle Scholar
  9. 9.
    Zhang, R., Zeng, D., Zhong, S., Yu, Y.: Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays. Appl. Math. Comput. 310, 57–74 (2017)MathSciNetGoogle Scholar
  10. 10.
    Zheng, M., et al.: Finite-time projective synchronization of memristor-based delay fractional-order neural networks. Nonlinear Dyn. 89(4), 2641–2655 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Guo, Z., Wang, J., Yan, Z.: Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw. 48, 158–172 (2013)CrossRefzbMATHGoogle Scholar
  12. 12.
    Wen, S., Huang, T., Zeng, Z., Chen, Y., Li, P.: Circuit design and exponential stabilization of memristive neural networks. Neural Netw. 63, 48–56 (2015)CrossRefzbMATHGoogle Scholar
  13. 13.
    Abdurahman, A., Jiang, H., Teng, Z.: Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control. J. Frankl. Inst. 353(13), 2859–2880 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Duan, S., Hu, X., Dong, Z., Wang, L., Mazumder, P.: Memristor-based cellular nonlinear/neural network: design, analysis, and applications. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1202–1213 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhang, H., Wang, Z., Liu, D.: A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25, 1229–1262 (2014)CrossRefGoogle Scholar
  16. 16.
    Wu, A., Zeng, Z.: Lagrange stability of memristive neural networks with discrete and distributed delays. IEEE Trans. Neural Netw. Learn. Syst. 25(4), 690–703 (2014)CrossRefGoogle Scholar
  17. 17.
    Wang, X., Li, C., Huang, T., Chen, L.: Dual-stage impulsive control for synchronization of memristive chaotic neural networks with discrete and continuously distributed delays. Neurocomputing 149, 621–628 (2015)CrossRefGoogle Scholar
  18. 18.
    Zhang, G., Shen, Y., Yin, Q., Sun, J.: Passivity analysis for memristor-based recurrent neural networks with discrete and distributed delays. Neural Netw. 61, 49–58 (2015)CrossRefzbMATHGoogle Scholar
  19. 19.
    Jiang, P., Zeng, Z., Chen, J.: Almost periodic solutions for a memristor-based neural networks with leakage, time-varying and distributed delays. Neural Netw. 68, 34–45 (2015)CrossRefzbMATHGoogle Scholar
  20. 20.
    Wang, L., Zeng, Z., Ge, M.-F., Hu, J.: Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays. Neural Netw. 105, 65–74 (2018)CrossRefGoogle Scholar
  21. 21.
    Song, Q., Zhao, Z., Liu, Y.: Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168, 1044–1050 (2015)CrossRefGoogle Scholar
  22. 22.
    Song, Q., Yu, Q., Zhao, Z., Liu, Y., Alsaadi, F.E.: Dynamics of complex-valued neural networks with variable coefficients and proportional delays. Neurocomputing 275, 2762–2768 (2018)CrossRefGoogle Scholar
  23. 23.
    Song, Q., Yu, Q., Zhao, Z., Liu, Y., Alsaadi, F.E.: Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties. Neural Netw. 103, 55–62 (2018)CrossRefGoogle Scholar
  24. 24.
    Angelaki, D.E., Correia, M.J.: Models of membrane resonance in pigeon semicircular canal type II hair cells. Biol. Cybern. 65(1), 1–10 (1991)CrossRefGoogle Scholar
  25. 25.
    Wheeler, D.W., Schieve, W.C.: Stability and chaos in an inertial two-neuron system. Physica D 105, 267–284 (1997)CrossRefzbMATHGoogle Scholar
  26. 26.
    Liu, Q., Liao, X., Liu, Y., Zhou, S., Guo, S.: Dynamics of an inertial two-neuron system with time delay. Nonlinear Dyn. 58(3), 573 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Cao, J., Wan, Y.: Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw. 53, 165–172 (2014)CrossRefzbMATHGoogle Scholar
  28. 28.
    Lakshmanan, S., et al.: Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Trans. Neural Netw. Learn. Syst. 29, 195–207 (2018)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Tu, Z., Cao, J., Hayat, T.: Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays. Neurocomputing 171, 524–531 (2016)CrossRefGoogle Scholar
  30. 30.
    Zhang, W., Li, C., Huang, T., Tan, J.: Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Comput. Appl. 26, 1781–1787 (2015)CrossRefGoogle Scholar
  31. 31.
    Li, X., Li, X., Hu, C.: Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method. Neural Netw. 96, 91–100 (2017)CrossRefGoogle Scholar
  32. 32.
    Kwon, O.M., Park, J.H., Lee, S.M., Cha, E.J.: New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays. Nonlinear Dyn. 76(1), 221–236 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Wang, L., Zeng, Z., Hu, J., Wang, X.: Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations. Neural Netw. 87, 122–131 (2017)CrossRefGoogle Scholar
  34. 34.
    Rakkiyappan, R., Premalatha, S., Chandrasekar, A., Cao, J.: Stability and synchronization analysis of inertial memristive neural networks with time delays. Cognit. Neurodyn. 10, 437–451 (2016)CrossRefGoogle Scholar
  35. 35.
    Zhang, G., Zeng, Z.: Exponential stability for a class of memristive neural networks with mixed time-varying delays. Appl. Math. Comput. 321, 544–554 (2018)MathSciNetGoogle Scholar
  36. 36.
    Zhang, W., Huang, T., He, X., Li, C.: Global exponential stability of inertial memristor-based neural networks with time-varying delays and impulses. Neural Netw. 95, 102–109 (2017)CrossRefGoogle Scholar
  37. 37.
    Tu, Z., Cao, J., Alsaedi, A., Alsaadi, F.: Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw. 88, 125–133 (2017)CrossRefGoogle Scholar
  38. 38.
    Zhang, G., Zeng, Z., Hu, J.: New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays. Neural Netw. 97, 183–191 (2018)CrossRefGoogle Scholar
  39. 39.
    Xiao, Q., Huang, Z., Zeng, Z.: Passivity analysis for memristor-based inertial neural networks with discrete and distributed dlays. IEEE Trans. Syst. Man Cybern. Syst.  https://doi.org/10.1109/TSMC.2017.2732503
  40. 40.
    Huang, D., Jiang, M., Jian, J.: Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control. Neurocomputing 266, 527–539 (2017)CrossRefGoogle Scholar
  41. 41.
    Wei, R., Cao, J., Alsaedi, A.: Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays. Cognit. Neurodyn. 12, 121–134 (2018)CrossRefGoogle Scholar
  42. 42.
    Gong, S., Yang, S., Guo, Z., Huang, T.: Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller. Neural Netw. 102, 138–148 (2018)CrossRefGoogle Scholar
  43. 43.
    Wang, L., Ge, M.-F., Zeng, Z., Hu, J.: Finite-time robust consensus of nonlinear disturbed multiagent systems via two-layer event-triggered control. Inf. Sci. 466, 270–283 (2018)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Zhang, R., Liu, X., Zeng, D., Zhong, S., Shi, K.: A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems. Fuzzy Sets Syst.  https://doi.org/10.1016/j.fss.2017.12.010
  45. 45.
    Zhang, R., Zeng, D., Park, J.H., Liu, Y., Zhong, S.: A new approach to stabilization of chaotic systems with nonfragile fuzzy proportional retarded sampled-data control. IEEE Trans. Cybern.  https://doi.org/10.1109/TCYB.2018.2831782
  46. 46.
    Filippov, A.F.: Differential Equations with Discontinuous Right-hand Sides. Kluwer, Dordrecht (1988)CrossRefzbMATHGoogle Scholar
  47. 47.
    Clarke, F.H., Ledyaev, Y.S., Stem, R.J., Wolenski, R.R.: Nonsmooth Analysis and Control Theory. Springer, New York (1998)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Leimin Wang
    • 1
    • 2
    Email author
  • Ming-Feng Ge
    • 3
  • Junhao Hu
    • 4
  • Guodong Zhang
    • 4
  1. 1.School of AutomationChina University of GeosciencesWuhanChina
  2. 2.Hubei key Laboratory of Advanced Control and Intelligent Automation for Complex SystemsWuhanChina
  3. 3.School of Mechanical Engineering and Electronic InformationChina University of GeosciencesWuhanChina
  4. 4.College of Mathematics and StatisticsSouth-Central University for NationalitiesWuhanChina

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