Skip to main content
SpringerLink
Log in

Design of Stochastic Passivity and Passification for Delayed BAM Neural Networks with Markov Jump Parameters via Non-uniform Sampled-Data Control

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper investigates the issue of passivity and passification for delayed Markov jump bidirectional associate memory (BAM)-Type neural networks via non-uniform sampled-data control. By utilizing the Lyapunov–Krasovskii functional strategy, a novel delay-dependent passivity criterion is developed with respect to linear matrix inequalities to guarantee the Markov jump delayed BAM neural frameworks to be passive. At that point, in view of the got passivity conditions, the passification issue is further tackled by planning a mode-dependent non-uniform sampled-data controller design is presented. Finally, a numerical example is provided to illustrate the applicability and effectiveness of the theoretical result.

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

Similar content being viewed by others

References

  1. Qiang Z, Wei X, Jin X (2005) Global asymptotic stability analysis of neural networks with time-varying delays. Neural Process Lett 21(1):61–71

    Article  Google Scholar 

  2. Hua M, Liu X, Deng F, Fei J (2010) New results on robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. Neural Process Lett 32(3):219–233

    Article  Google Scholar 

  3. Kwon OM, Lee S-M, Park JH, Cha E-J (2012) New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput 218(19):9953–9964

    MathSciNet  MATH  Google Scholar 

  4. Gunasekaran N, Thoiyab NM, Muruganantham P, Rajchakit G, Unyong B (2020) Novel results on global robust stability analysis for dynamical delayed neural networks under parameter uncertainties. IEEE Access 8:178108–178116

    Article  Google Scholar 

  5. Ali MS, Gunasekaran N (2018) State estimation of static neural networks with interval time-varying delays and sampled-data control. Comput Appl Math 37(1):183–201

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  7. Ali MS, Gunasekaran N, Cao J (2019) Sampled-data state estimation for neural networks with additive time–varying delays. Acta Math Sci 39(1):195–213

    Article  MathSciNet  Google Scholar 

  8. Tong Y, Tong D, Chen Q, Zhou W (2020) Finite-time state estimation for nonlinear systems based on event-triggered mechanism. Circuit Syst Signal Process 39(7):3737–3757

    Article  Google Scholar 

  9. Gunasekaran N, Zhai G, Qiang Yu (2020) Sampled-data synchronization of delayed multi-agent networks and its application to coupled circuit. Neurocomputing 413:499–511

    Article  Google Scholar 

  10. Ali MS, Gunasekaran N, Zhu Q (2017) State estimation of t–s fuzzy delayed neural networks with markovian jumping parameters using sampled-data control. Fuzzy Sets Syst 306:87–104

    Article  MathSciNet  Google Scholar 

  11. Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26(23):4947–4960

    Article  Google Scholar 

  12. Gopalsamy K, He X-Z (1994) Delay-independent stability in bidirectional associative memory networks. IEEE Trans Neural Netw 5(6):998–1002

    Article  Google Scholar 

  13. Cao J, Dong M (2003) Exponential stability of delayed bi-directional associative memory networks. Appl Math Comput 135(1):105–112

    MathSciNet  MATH  Google Scholar 

  14. Arik S (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays. IEEE Trans Neural Netw 16(3):580–586

    Article  Google Scholar 

  15. Ali MS, Balasubramaniam P (2009) Robust stability of uncertain fuzzy Cohen–Grossberg BAM neural networks with time-varying delays. Expert Syst Appl 36(7):10583–10588

    Article  Google Scholar 

  16. Mathiyalagan K, Sakthivel R, Anthoni SM (2012) New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays. Commun Nonlinear Sci Numer Simul 17(3):1392–1407

    Article  MathSciNet  Google Scholar 

  17. Bao H, Cao J (2012) Exponential stability for stochastic BAM networks with discrete and distributed delays. Appl Math Comput 218(11):6188–6199

    MathSciNet  MATH  Google Scholar 

  18. Sakthivel R, Vadivel P, Mathiyalagan K, Arunkumar A, Sivachitra M (2015) Design of state estimator for bidirectional associative memory neural networks with leakage delays. Inf Sci 296:263–274

    Article  MathSciNet  Google Scholar 

  19. Belevitch V (1968) Classical network theory. Holden-day 7

  20. Luo M, Zhong S (2012) Passivity analysis and passification of uncertain Markovian jump systems with partially known transition rates and mode-dependent interval time-varying delays. Comput Math Appl 63(7):1266–1278

    Article  MathSciNet  Google Scholar 

  21. Balasubramaniam P, Nagamani G (2012) Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays. Expert Syst Appl 39(1):732–742

    Article  Google Scholar 

  22. Guo Z, Wang J, Yan Z (2014) Passivity and passification of memristor-based recurrent neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25(11):2099–2109

    Article  Google Scholar 

  23. Ali MS, Meenakshi K, Gunasekaran N (2018) Finite time \(H_\infty \) boundedness of discrete-time Markovian jump neural networks with time-varying delays. Int J Control Autom Syst 16(1):181–188

    Article  Google Scholar 

  24. Zhang H, Ji H, Ye Z, Senping T (2016) Passivity analysis of Markov jump BAM neural networks with mode-dependent mixed time-delays via piecewise-constant transition rates. J Franklin Inst 353(6):1436–1459

    Article  MathSciNet  Google Scholar 

  25. Kao Y, Shi L, Xie J, Karimi HR (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Netw 63:18–30

    Article  Google Scholar 

  26. Xu C, Tong D, Chen Q, Zhou W, Shi P (2019) Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE Trans Syst Man Cybernet Syst (2019)

  27. Xu C, Tong D, Chen Q, Zhou W (2020) Asynchronous control of T-S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity. Opt Control Appl Methods 41(2):587–604

    Article  MathSciNet  Google Scholar 

  28. Gunasekaran N, Ali MS (2016) Sampled-data state estimation for delayed Markovian jump neural networks based on passive theory. In: 2016 international conference on inventive computation technologies (ICICT), vol 3, pp 1–5. IEEE

  29. Ali MS, Meenakshi K, Gunasekaran N, Murugan K (2018) Dissipativity analysis of discrete-time Markovian jumping neural networks with time-varying delays. J Differ Equ Appl 24(6):859–871

    Article  MathSciNet  Google Scholar 

  30. Gunasekaran N, Saravanakumar R, Joo YH, Kim HS (2019) Finite-time synchronization of sampled-data T–S fuzzy complex dynamical networks subject to average dwell-time approach. Fuzzy Sets Syst 374:40–59

    Article  MathSciNet  Google Scholar 

  31. Wang J, Tian L (2019) Stability of inertial neural network with time-varying delays via sampled-data control. Neural Process Lett 50(2):1123–1138

    Article  MathSciNet  Google Scholar 

  32. Gunasekaran N, Ali MS, Pavithra S (2019) Finite-time \({L}_\infty \) performance state estimation of recurrent neural networks with sampled-data signals. Neural Process Lett 1–14

  33. Ali MS, Gunasekaran N, Joo YH (2019) Sampled-data state estimation of neutral type neural networks with mixed time-varying delays. Neural Process Lett 50(1):357–378

    Article  Google Scholar 

  34. Ali MS, Gunasekaran N, Aruna B (2017) Design of sampled-data control for multiple-time delayed generalised neural networks based on delay-partitioning approach. Int J Syst Sci 48(13):2794–2810

    Article  MathSciNet  Google Scholar 

  35. Gunasekaran N, Saravanakumar R, Ali MS, Zhu Q (2019) Exponential sampled-data control for T–S fuzzy systems: application to Chua’s circuit. Int J Syst Sci 50(16):2979–2992

    Article  MathSciNet  Google Scholar 

  36. Gunasekaran N, Joo YH (2020) Nie-Tan fuzzy method of fault-tolerant wind energy conversion systems via sampled-data control. IET Control Theory Appl 14(11):1516–1523

    Article  Google Scholar 

  37. Ma C, Zeng Q, Zhang L, Zhu Y (2014) Passivity and passification for Markov jump genetic regulatory networks with time-varying delays. Neurocomputing 136:321–326

    Article  Google Scholar 

  38. Li L, Xing Z, He B (2016) Non-uniform sampled-data control for stochastic passivity and passification of Markov jump genetic regulatory networks with time-varying delays. Neurocomputing 171:434–443

    Article  Google Scholar 

  39. de Souza CE, Trofino A, Barbosa KA (2004) Mode-independent H/sub /spl infin// filters for hybrid Markov linear systems. In: 2004 43rd IEEE conference on decision and control (CDC) (IEEE Cat. No.04CH37601), vol. 1, pp. 947–952 (2004)

  40. Ma C, Zeng Q, Zhang L, Zhu Y (2014) Passivity and passification for Markov jump genetic regulatory networks with time-varying delays. Neurocomputing 136:321–326

    Article  Google Scholar 

  41. Peng C, Tian Y-C (2008) Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. J Comput Appl Math 214(2):480–494

    Article  MathSciNet  Google Scholar 

  42. Thuan MV, Trinh H, Hien LV (2016) New inequality-based approach to passivity analysis of neural networks with interval time-varying delay. Neurocomputing 194:301–307

    Article  Google Scholar 

  43. Ali MS, Yogambigai J, Saravanan S, Elakkia S (2019) Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays. J Comput Appl Math 349:142–156

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama, 337-8570, Japan

    Nallappan Gunasekaran

  2. Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, 632115, India

    M. Syed Ali

Authors
  1. Nallappan Gunasekaran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Syed Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Syed Ali.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

The work of author was supported by CSIR . 25(0274)/17/EMR-II dated 27/04/2017.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gunasekaran, N., Ali, M.S. Design of Stochastic Passivity and Passification for Delayed BAM Neural Networks with Markov Jump Parameters via Non-uniform Sampled-Data Control. Neural Process Lett 53, 391–404 (2021). https://doi.org/10.1007/s11063-020-10394-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-020-10394-6

Keywords

Search

Navigation