Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

Article
  • 8 Downloads

Abstract

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results

Keywords

BAM Neural networks event-triggered communication scheme linear matrix inequality Lyapunov-Krasovskii functional Markovian jumping parameters time varying delay 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. Kosko, “Bidirectional associative memories,” IEEE Trans. Syst., Man, Cybern., vol. 18, no. 1, pp. 49–60, February 1988. [click]MathSciNetCrossRefGoogle Scholar
  2. [2]
    B. Kosko, “Adaptive bi-directional associative memories,” Appl. Opt., vol. 26, no. 23, pp. 4947–4960, December 1987.CrossRefGoogle Scholar
  3. [3]
    M. S. Ali, R. Saravanakumar, and J. Cao, “New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays,” Neurocomputing, vol. 171, no. 1, pp. 1533–1547, January 2016.Google Scholar
  4. [4]
    S. Arik, “Global asymptotic stability of hybrid BAMneural networks with time delays,” Phys. Lett. A, vol. 351, no. 1-2, pp. 85–91, February 2006. [click]CrossRefMATHGoogle Scholar
  5. [5]
    S. Arik, “Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays,” IEEE Trans. Neural Netw., vol. 16, no. 3, pp. 580–586, May 2005. [click]CrossRefGoogle Scholar
  6. [6]
    J. H. Park, “Robust stability of bidirectional associative memory neural networks with time delays,” Phys. Lett. A, vol. 349, no. 6, pp. 494–499, January 2006.CrossRefGoogle Scholar
  7. [7]
    B. Liu and P. Shi, “Delay-range-dependent stability for fuzzy BAM neural networks with time-varying delays,” Phys. Lett. A, vol. 373, no. 21, pp 1830–1838, May 2009. [click]MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    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. [click]MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    M. S. Ali, R. Saravanakumar, and S. Arik, “Delaydependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed timevarying delays,” Neurocomputing, vol. 158, pp 167–173, June 2015.CrossRefGoogle Scholar
  10. [10]
    B. Niu, X. Zhao, L. Zhang, and H. Li, “p-Times differentiable unbounded functions for robust control of uncertain switched nonlinear systems with tracking constraints,” Int. J. Robust Nonlinear Control, vol. 25, no. 16, pp 2965–2983, November 2015. [click]MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    J. H. Park, C. H. Park, O. M. Kwon, and S. M. Lee, “A new stability criterion for bidirectional associative memory neural networks of neutral-type,” Appl. Math. Comput. vol. 199, no. 2, pp. 716–722, June 2008. [click]MathSciNetMATHGoogle Scholar
  12. [12]
    J. Liu and G. Zong, “New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type,” Neurocomputing, vol. 72, no. 10-12, pp 2549–2555, June 2009. [click]CrossRefGoogle Scholar
  13. [13]
    M. Kovacic, “Markovian neural networks,” Biol. Cybern., vol. 64, no. 4, pp 337–342, February 1991. [click]MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    M. Syed Ali, “Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays,” Neurocomputing, vol. 149, pp 1280–1285, February 2015. [click]CrossRefGoogle Scholar
  15. [15]
    Y. G. Kao, C. H. Wang, J. Xie, H. R. Karimi, and W. Li, “H∞ sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters,” Inform. Sci., vol. 314, no. 1, pp 200–211, September 2015. [click]MathSciNetCrossRefGoogle Scholar
  16. [16]
    P. Balasubramaniam and V. Vembarasan, “Robust stability of uncertain fuzzy BAM neural networks of neutraltype with Markovian jumping parameters and impulses,” Comput. Math. Appl., vol. 62, no. 4, pp 1838–1861, August 2011. [click]MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    B. Niu and L. Li, “Adaptive backstepping-based neural tracking control for MIMO nonlinear switched systems subject to input delays,” IEEE Trans. Neural Netw. Learn. Syst., April 2017. DOI: 10.1109/TNNLS.2017.2690465.Google Scholar
  18. [18]
    R. Saravanakumar, M. S. Ali, H. Huang, J. Cao, and Y. H. Joo, “Robust H∞ state-feedback control for nonlinear uncertain systems with mixed time-varying delays,” Int. J. Control Autom. Syst., vol. 16, no. 1, pp. 225–233, February 2018.CrossRefGoogle Scholar
  19. [19]
    B. Niu, H. Li, T. Qin, and H. R. Karimi, “Adaptive NN dynamic surface controller design for nonlinear purefeedback switched systems with time-delays and quantized input,” IEEE Trans. Syst., Man, Cybern., Syst., DOI:10.1109/TSMC.2017.2696710, May 2017.Google Scholar
  20. [20]
    E. Arslan, R. Vadivel, M. Syed Ali, and S. Arik, “Eventtriggered H∞ filtering for delayed neural networks via sampled-data,” Neural Netw. vol. 91, pp 11–21, July 2017. [click]CrossRefGoogle Scholar
  21. [21]
    J. Wang, X. M. Zhang, and Q. L. Han, “Event-triggered generalized dissipativity filtering for neural networks with time-varying delays,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 1, pp 77–88, January 2016. [click]MathSciNetCrossRefGoogle Scholar
  22. [22]
    J. Zhang and C. Peng, “Synchronization of master-slave neural networks with a decentralized even triggered communication scheme,” Neurocomputing, vol. 173, no. 3, pp 1824–1831, January 2016. [click]CrossRefGoogle Scholar
  23. [23]
    S. Senan, M. Syed Ali, R. Vadivel, and S. Arik, “Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays,” Neural Netw., vol. 86, pp. 32–41, February 2017. [click]CrossRefGoogle Scholar
  24. [24]
    M. Mazo and M. Cao, “Asynchronous decentralized eventtriggered control,” Automatica, vol. 50, no. 12, pp 3197–3203, December 2014.MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    M. C. F. Donkers and W. P. M. H. Heemels, “Outputbased event-triggered control with garanteed L∞-gain and improved and decentralized event-triggering,” IEEE Trans. Autom. Control, vol. 57, no. 6, pp 1362–1376, June 2012. [click]CrossRefMATHGoogle Scholar
  26. [26]
    H. Wang, P. Shi, and R. K. Agarwal, “Network-based event-triggered filtering for Markovian jump systems,” Int. J. Control, vol. 89, no. 1, pp 1096–1110, November 2015. [click]MathSciNetMATHGoogle Scholar
  27. [27]
    H. Zhang, J. Cheng, H. Wang, Y. Chen, and H. Xiang, “Robust finite-time event-triggered H∞ boundedness for network-based Markovian jump nonlinear systems,” ISA Trans. Vol. 63, pp 32–38, July 2016.CrossRefGoogle Scholar
  28. [28]
    H. Li, Z. Zuo, and Y. Wang, “Event triggered control for Markovian jump systems with partially unknown transition probabilities and actuator saturation,” J. Frankl. Inst., vol. 353, no. 8, pp 1848–1861, May 2016.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    Y. Tan, D. Du, and Q. Qi, “State estimation for Markovian jump systems with an event-triggered communication scheme,” Circuits Syst. Signal Process., vol. 36, no. 1, pp 1–23, January 2017.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThiruvalluvar UniversityVelloreIndia
  2. 2.School of Electrical EngineeringChungbuk National University, Chungdae-ro 1CheongjuKorea

Personalised recommendations