Skip to main content
Log in

Robust Stabilization of Memristor-based Coupled Neural Networks with Time-varying Delays

  • Intelligent Control and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

The robust stabilization problem of memristor-based coupled neural networks (MNNs) is addressed in this paper. Firstly, the fuzzy model of MNNs is obtained by considering the properties of memristor and corresponding circuit, some predictable assumptions on the boundedness and Lipschitz continuity of activation functions are formulated. Secondly, based on T-S fuzzy theory and Lyapunov-Krasovskii functional method, robust stabilization criteria are derived in form of linear matrix inequalities (LMIs). Finally a numerical example is presented to demonstrate the effectiveness of the proposed robust stabilization criteria, which well supports theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. O. Chua, “Memristor-the missing circuit element,” IEEE Transactions on Circuit Theory, vol. 18, no. 5, pp. 507–519, September 1971.

    Article  Google Scholar 

  2. D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature, vol. 453, no. 7191, pp. 80–83, June 2008.

    Article  Google Scholar 

  3. H. B. Bao, J. H. Park, and J. D. Cao, “Adaptive synchronization of fractional-order memristor-based neural networks with time delay,” Nonlinear Dynamics, vol. 82, no. 3, pp. 1343–1354, Novermber 2015.

    Article  MathSciNet  Google Scholar 

  4. R. M. Zhang, D. Q. Zeng, S. M. Zhong, and Y. B. Yu, “Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays,” Applied Mathematics and Computation, vol. 310, pp. 57–74, October 2017.

    Article  MathSciNet  Google Scholar 

  5. C. J. Xu and P. L. Li, “Periodic dynamics for memristorbased bidirectional associative memory neural networks with leakage delays and time-varying delays,” International Journal of Control Automation and Systems, vol. 16, no. 2, pp. 535–549, April 2018.

    Article  MathSciNet  Google Scholar 

  6. H. B. Bao, J. D. Cao, and J. Kurths, “State estimation of fractional-order delayed memristive neural networks,” Nonlinear Dynamics, vol. 94, no. 2, pp. 1215–1225, October 2018.

    Article  Google Scholar 

  7. S. G. Hu, Y. Liu, Z. Liu, T. P. Chen, Q. Yu, L. J. Deng, Y. Yin, and S. Hosaka, “Synaptic long-term potentiation realized in pavlov’s dog model based on a niox-based memristor,” Journal of Applied Physics, vol. 116, no. 21, pp. 214502, December 2014.

    Article  Google Scholar 

  8. R. M. Zhang, D. Q. Zeng, S. M. Zhong, K. B. Shi, and J. Z. Cui, “New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic lur’e systems,” Nonlinear Analysis Hybrid Systems, vol. 29, pp. 303–321, August 2018.

    Article  MathSciNet  Google Scholar 

  9. H. Kim, M. P. Sah, C. J. Yang, T. Roska, and L. O. Chua, “Neural synaptic weighting with a pulse-based memristor circuit,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 1, pp. 148–158, January 2012.

    Article  MathSciNet  Google Scholar 

  10. R. M. Zhang, D. Q. Zeng, and S. M. Zhong, “Novel masterslave synchronization criteria of chaotic lur’e systems with time delays using sampled-data control,” Journal of the Franklin Institute, vol. 354, no. 12, pp. 4930–4954, August 2017.

    Article  MathSciNet  Google Scholar 

  11. H. B. Bao, J. D. Cao, J. Kurths, A. Alsaedi, and B. Ahmad, “H state estimation of stochastic memristor-based neural networks with time-varying delays,” Neural Networks, vol. 99, pp. 79–91, March 2018.

    Article  Google Scholar 

  12. Y. S. Tan, S. Y. Tang, and X. F. Chen, “Robust stability analysis of impulsive complex-valued neural networks with time delays and parameter uncertainties,” Advances in Difference Equations, vol. 62, pp. 1–18, February 2018.

    MathSciNet  MATH  Google Scholar 

  13. Q. H. Fu, J. Y. Cai, S. M. Zhong, Y. B. Yu, and Y. N. Shan, “Input-to-state stability of discrete-time memristive neural networks with two delay components,” Neurocomputing, vol. 329, pp. 1–11, February 2019.

    Article  Google Scholar 

  14. H. B. Bao, J. H. Park, and J. D. Cao, “Exponential synchronization of coupled stochastic memristor-based neural networks with time-varying probabilistic delay coupling and impulsive delay,” IEEE transactions on neural networks and learning systems, vol. 27, no. 1, pp. 190–201, January 2016.

    Article  MathSciNet  Google Scholar 

  15. J. Liu and R. Xu, “Global dissipativity analysis for memristor-based uncertain neural networks with time delay in the leakage term,” International Journal of Control Automation and Systems, vol. 15, no. 5, pp. 2406–2415, October 2017.

    Article  Google Scholar 

  16. L. M. Wang, Y. Shen, and G. D. Zhang, “Finite-time stabilization and adaptive control of memristor-based delayed neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 11, pp. 2648–2659, November 2017.

    Article  MathSciNet  Google Scholar 

  17. R. Rakkiyappan, A. Chandrasekar, and S. Lakshmanan, “Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays,” International Journal of Systems Science, vol. 47, no. 10, pp. 2247–2263, July 2016.

    Article  MathSciNet  Google Scholar 

  18. X. F. Chen, L. J. Li, and Z. S. Li, “Robust stability analysis of quaternion-valued neural networks via LMI approach,” Advances in Difference Equations, pp. 131, April 2018.

    Google Scholar 

  19. R. M. Zhang, X. Z. Liu, D. Q. Zeng, S. M. Zhong, and K. B. Shi, “A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems,” Fuzzy Sets and Systems, vol. 344, pp. 108–128, August 2018.

    Article  MathSciNet  Google Scholar 

  20. A. L. Wu, S. P. Wen, and Z. G. Zeng, “Synchronization control of a class of memristor-based recurrent neural networks,” Fuzzy Sets and Systems, vol. 183, no. 1, pp. 106–116, January 2012.

    MathSciNet  MATH  Google Scholar 

  21. S. P. Wen, G. Bao, Z. G. Zeng, Y. R. Chen, and T. W. Huang, “Global exponential synchronization of memristorbased recurrent neural networks with time-varying delays,” Neural Networks, vol. 48, pp. 195–203, December 2013.

    Article  Google Scholar 

  22. S. P. Wen, T. W. Huang, Z. G. Zeng, Y. R. Chen, and P. Li, “Circuit design and exponential stabilization of memristive neural networks,” Neural Networks, vol. 63, pp. 48–56, May 2015.

    Article  Google Scholar 

  23. A. C. Torrezan, J. P. Strachan, G. Medeiros-Ribeiro, and R. S. Williams, “Sub-nanosecond switching of a tantalum oxide memristor,” Nanotechnology, vol. 22, no. 48, pp. 485203, December 2011.

    Article  Google Scholar 

  24. D. J. Kim, H. Lu, S. Ryu, C. W. Bark, C. B. Eom, E. Y. Tsymbal and A. Gruverman, “Ferroelectric tunnel memristor,” Nano letters, vol. 12, no. 11, pp. 5697–5702, November 2012.

    Article  Google Scholar 

  25. Y. T. Wang, X. Zhang, and Z. R. Hu, “Delay-dependent robust H filtering of uncertain stochastic genetic regulatory networks with mixed time-varying delays,” Nano Letters, vol. 12, no. 11, pp. 5697–5702, November 2012.

    Article  Google Scholar 

  26. Y. Liu, L. S. Hu, and P. Shi, “A novel approach on stabilization for linear systems with time-varying input delay,” Applied Mathematics and Computation, vol. 218, no. 10, pp. 5937–5947, January 2012.

    Article  MathSciNet  Google Scholar 

  27. P. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica, vol. 47, no. 1, pp. 235–238, January 2011.

    Article  MathSciNet  Google Scholar 

  28. J. Li, M. F. Hu, and L. X. Guo, “Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays,” Neurocomputing, vol. 138, pp. 92–98, August 2014.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qianhua Fu.

Additional information

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Editor Jessie (Ju H.) Park. This work was supported in part by the Scientific Research Project of Sichuan Provincial Education Department (18ZB0572), in part by the National Natural Science Foundation of China under Grants 61533006.

Qianhua Fu received his B.S. degree in electronic information engineering from Chongqing University of Technology, China, in 2003, and his M.S. degree in communication and information systems from University of Electronic Science and Technology of China (UESTC) in 2010. He was a R&D engineer in HUAWEI company from 2010 to 2014. He is currently pursuing a Ph.D. degree in UESTC and working as a senior engineer at Xihua University. His main research interests are memristor neural network, RF circuits and wireless systems, and signal processing in modern communication.

Jingye Cai received his B.S. degree from Sichuan University in 1983, and his M.S. degree from the University of Electronic Science and Technology of China (UESTC) in 1990. He is currently a professor with the School of Software and Information Engineering, UESTC. His research interests include nonlinear circuits and systems (memristor), communication signal processing, RF and wireless systems.

Shouming Zhong was born on November 5, 1955. He graduated from University of Electronic Science and Technology of China (UESTC), majoring Applied Mathematics on Differential Equation. He is a professor of School of Mathematical Sciences, UESTC, since June 1997-present. His research interest is stability theorem and its application research of the differential system, the robustness control, and neural network.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, Q., Cai, J. & Zhong, S. Robust Stabilization of Memristor-based Coupled Neural Networks with Time-varying Delays. Int. J. Control Autom. Syst. 17, 2666–2676 (2019). https://doi.org/10.1007/s12555-018-0936-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-0936-6

Keywords

Navigation