Skip to main content
SpringerLink
Log in

Passivity analysis of coupled inertial neural networks with time-varying delays and impulsive effects

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

This paper is devoted to the passivity analysis of an array model for coupled inertial delayed neural networks (NNs) with impulses under different network structures, namely directed and undirected topologies. Firstly, utilising the information of eigenvectors for the directed coupling matrix, a new Lyapunov functional is constructed, by which, together with the aid of some inequality techniques and network characteristics, the two sets of sufficient criteria are established to, respectively, guarantee the strictly input passivity and strictly output passivity of the impulsive network with directed coupling. Secondly, benefited from the properties of the undirected coupling matrix, some more concise conditions that are easier to be verified for the passivities of the undirected coupled network accompanied by impulsive effects are proposed. Finally, two numerical examples are designed to execute the verification of the derived theoretical results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. H A Rowley, S Baluja and T Kanade, IEEE Trans. Pattern Anal. 20, 23 (1998)

    Article  Google Scholar 

  2. A S Miller, B H Blott and T K Hames, Med. Biol. Eng. Comput. 30, 449 (1992)

    Article  Google Scholar 

  3. B K Bose, Proc. IEEE 82(8), 1303 (1994)

    Article  Google Scholar 

  4. R Manivannan, R Samidurai, J D Cao, A Alsaedi and F E Alsaadi, Neural Netw. 87, 149 (2017)

    Article  Google Scholar 

  5. J D Cao and M Xiao, IEEE Trans. Neural Netw. 18(2), 416 (2007)

    Article  Google Scholar 

  6. R X Li, J D Cao, A Alsaedi and B Ahmad, J. Franklin Inst. 354(7), 3021 (2017)

    Article  MathSciNet  Google Scholar 

  7. J D Cao and R X Li, Sci. China Inf. Sci. 60(3), 032201 (2017)

    Article  MathSciNet  Google Scholar 

  8. K Babcock and R Westervelt, Physica D 23, 464 (1986)

    Article  ADS  Google Scholar 

  9. D E Angelaki and M J Correia, Biol. Cybern. 65, 1 (1991)

    Article  Google Scholar 

  10. J F Ashmore and D Attwell, Proc. R. Soc. London. B: Biol. Sci. 226, 325 (2014)

    Article  ADS  Google Scholar 

  11. H Y Zhao, L Chen and X Yu, Acta Phys. Sin. 60, 1 (2011)

    Google Scholar 

  12. C Li, G Chen, X Liao and J Yu, Eur. Phys. J. B 41, 337 (2004)

    Article  ADS  Google Scholar 

  13. M Prakash, P Balasubramaniama and S Lakshmananc, Neural Netw. 83, 86 (2016)

    Article  Google Scholar 

  14. J T Qi, C D Li and T W Huang, Neurocomputing 161, 162 (2015)

    Article  Google Scholar 

  15. J Q Hu, J D Cao, A Alofi, A AL-Mazrooei and A Elaiw, Cogn. Neurodyn. 9, 341 (2015)

    Article  Google Scholar 

  16. S Dharani, R Rakkiyappan and J H Park, Neurocomputing 227, 101 (2017)

    Article  Google Scholar 

  17. S Lakshmanan, M Prakash, C P Lim, R Rakkiyappan, P Balasubramaniam and S Nahavandi, IEEE Trans. Neural Netw. Learn. Syst. 29(1), 195 (2018)

    Article  MathSciNet  Google Scholar 

  18. S Lakshmanan, C P Lim, M Prakash, S Nahavandi and P Balasubramaniam, Neurocomputing 230, 243 (2017)

    Article  Google Scholar 

  19. V Belevich, Classical network synthesis (Van Nostrand, New York, 1968)

    Google Scholar 

  20. G L Santosuosso, Automatica 33(4), 693 (1997)

    Article  MathSciNet  Google Scholar 

  21. C W Wu, IEEE Trans. Circuits Syst. I: Reg. Papers 48(10), 1257 (2001)

    Article  Google Scholar 

  22. L Xie, M Fu and H Li, IEEE Trans. Signal Process. 46(9), 2394 (1998)

    Article  ADS  Google Scholar 

  23. W Yu, IEEE Trans. Circuits Syst. I: Reg. Papers 46(7), 876 (1999)

    Article  Google Scholar 

  24. R X Li, J D Cao and Z W Tu, Neurocomputing 191, 249 (2016)

    Article  Google Scholar 

  25. R Sakthivel, A Arunkumar, K Mathiyalagan and S M Anthoni, Appl. Math. Comput. 218, 3799 (2011)

    MathSciNet  Google Scholar 

  26. J L Wang, H N Wu, T W Huang and S Y Ren, IEEE Trans. Cybern. 45(9), 1942 (2015)

    Article  Google Scholar 

  27. Z G Wu, P Shi, H Y Su and J Chu, IEEE Trans. Neural Netw. 22(10), 1566 (2011)

    Article  Google Scholar 

  28. J Q Lu, D W C Ho, J D Cao and J Kurths, IEEE Trans. Neural Netw. 22(2), 329 (2011)

    Article  Google Scholar 

  29. P C Wei, J L Wang, Y L Huang, B B Xu and S Y Ren, Neurocomputing 168, 13 (2015)

    Article  Google Scholar 

  30. X S Yang, J D Cao and D W C Ho, Cogn. Neurodyn. 9, 113 (2015)

    Article  Google Scholar 

  31. P Baldi and A F Atiya, IEEE Trans. Neural Netw. 5(5), 612 (1994)

    Article  Google Scholar 

  32. C I Byrnes, A Isidori and J C Willems, IEEE Trans. Autom. Control. 36(11), 1228 (1991)

    Article  Google Scholar 

  33. S I Niculescu and R Lozano, IEEE Trans. Autom. Control. 46(3), 460 (2001)

    Article  Google Scholar 

  34. W L Lu and T P Chen, Physica D 213(2), 214 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  35. W W Yu, J D Cao and J Wang, Neural Netw. 20, 810 (2007)

    Article  Google Scholar 

  36. S Boyd, L E Ghaoui, E Feron and V Balakrishnan, Linear matrix inequalities in system and control theory (SIAM, Philadelphia, 1994)

    Book  Google Scholar 

  37. W Zhang, C D Li, T W Huang and J Tan, Neural Comput. Appl. 26, 1781 (2015)

    Article  Google Scholar 

  38. J D Cao and Y Wan, Neural Netw. 53, 165 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This work was jointly supported by the National Natural Science Foundations of China (Nos 61573096, 61833005 and 11861060), the Engineering Foundation of Jiangsu Province of China (No. BRA2015286), the Fundamental Research Funds for the Central Universities, the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX17_0042), and the Youth Education Program of Xizang Minzu University (No. 18MDX01).

Author information

Authors and Affiliations

  1. School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, People’s Republic of China

    Xiao-shuai Ding & Jin-de Cao

  2. School of Education, Xizang Minzu University, Xianyang, 712082, People’s Republic of China

    Xiao-shuai Ding

  3. Electrical and Computer Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Fuad E Alsaadi

Authors
  1. Xiao-shuai Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin-de Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuad E Alsaadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin-de Cao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, Xs., Cao, Jd. & Alsaadi, F.E. Passivity analysis of coupled inertial neural networks with time-varying delays and impulsive effects. Pramana - J Phys 91, 69 (2018). https://doi.org/10.1007/s12043-018-1629-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-018-1629-7

Keywords

PACS Nos

Search

Navigation