Finite-time H Filtering for Discrete-time Markovian Jump BAM Neural Networks with Time-varying Delays



This paper deals with the problem of finite-time H filtering for discrete-time Markovian jump BAM neural networks with time-varying delays. To do this, firstly by choosing a suitable Lyapunov function and using Jensen inequality lemma, sufficient criteria are derived to guarantee that the resulting filtering error system is finitetime bounded. And then the gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter. Moreover, we assume that disturbances are described by the jumping parameters are generated from discrete-time homogeneous Markov process. Finally a numerical example is presented to show the effectiveness of the proposed method.


Bidirectional associative memory discrete time delay finite-time H control linear matrix inequality 


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  1. [1]
    B. Kosko, “Bidirectional associative memories,” IEEE Trans., vol. 18, pp. 49–60, 1988.MathSciNetGoogle Scholar
  2. [2]
    L. Zhou, “Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays,” Neurocomputing, vol. 161, pp. 99–106, 2015. [click]CrossRefGoogle Scholar
  3. [3]
    Q. Zhu, R. Rakkiyappan, and A. Chandrasekar, “Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control,” Neurocomputing, vol. 136, pp. 136–151, 2014. [click]CrossRefGoogle Scholar
  4. [4]
    A. Arunkumar, R. Sakthivel, K. Mathiyalagan, and S. M. Anthoni, “Robust state estimation for discrete-time BAM neural networks with time-varying delay,” Neurocomputing, vol. 131, pp. 171–178, 2014. [click]CrossRefMATHGoogle Scholar
  5. [5]
    Y. Wang and J. Cao, “Exponential stability of stochastic higher-order BAM neural networks with reaction-diffusion terms and mixed time-varying delays,” Neurocomputing, vol. 119, pp. 192–200, 2013.CrossRefGoogle Scholar
  6. [6]
    S. Lakshmanan, J. H. Park, T. H. Lee, H. Y. Jung, and R. Rakkiyappan, “Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays,” Appl. Math. Comput., vol. 219, pp. 9408–9423, 2013.MathSciNetMATHGoogle Scholar
  7. [7]
    D. Y. Wang and L. S. Li, “Mean-square stability analysis of discrete-time stochastic Markov jump recurrent neural networks with mixed delays,” Neurocomputing, vol. 189, pp. 171–178, 2016. [click]CrossRefGoogle Scholar
  8. [8]
    H. Shen, L. Su, and J. H. Park, “Extended passive filtering for discrete-time singular Markov jump systems with timevarying delays,” Signal Process., vol. 128, pp. 68–77, 2016.CrossRefGoogle Scholar
  9. [9]
    G. Nagamani and S. Ramasamy, “Dissipativity and passivity analysis for uncertain discrete-time stochastic Markovian jump neural networks with additive time-varying delays,” Neurocomputing, vol. 174, pp. 795–805, 2016.CrossRefMATHGoogle Scholar
  10. [10]
    B. Zhang and Y. Li, “Exponential filtering for distributed delay systems with Markovian jumping parameters,” Signal Process., vol. 93, pp. 206–216, 2013. [click]CrossRefGoogle Scholar
  11. [11]
    Y. Zhang, G. Cheng, and C. Liu, “Finite-time unbiased filtering for discrete jump time-delay systems,” Appl. Math. Model, vol. 38, pp. 3339–3349, 2014.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Y. Zhang, P. Shi, and H. R. Karimi, “Finite-time boundedness for uncertain discrete neural networks with timedelays and Morkovian jumps,” Neurocomputing, vol. 140, pp. 1–7, 2014.CrossRefGoogle Scholar
  13. [13]
    P.-L. Li, “Further results on robust delay-range-dependent stability criteria for uncertain neural networks with interval time-varying delay,” Int. J. Control Autom. Sys., vol. 13, no. 5, pp. 1140–1149,2015.CrossRefGoogle Scholar
  14. [14]
    Y. Du, W. Wen, S. Zhong, and N. Zhou, “Complete delaydecomposing approach to exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays,” Int. J. Control Autom. Sys., vol. 14, no. 4, pp. 1012–1020, 2016. [click]CrossRefGoogle Scholar
  15. [15]
    P. Dorato, “Short time stability in linear time-varying systems,” IRE International Convention Record, vol. 13, pp. 83–87, 1961.Google Scholar
  16. [16]
    Y. Ding, H. Liu, and J. Cheng, “filtering for a class of discrete-time singular Markovian jump systems with timevarying delays,” ISA Trans., vol. 53, pp. 1054–1060, 2014.CrossRefGoogle Scholar
  17. [17]
    W. Li and Y. Jia, “filtering for a class of nonlinear discrete-time systems based on unscented transform,” Signal Process., vol. 90, pp. 3301–3307, 2010.CrossRefMATHGoogle Scholar
  18. [18]
    G. Wang, H. Bo, and Q. Zhang, “H» filtering for timedelayed singular Markovian jump systems with timevarying switching: a quantized method,” Signal Process., vol. 109, pp. 14–24, 2015. [click]CrossRefGoogle Scholar
  19. [19]
    Y. Ma, L. Fu, Y. Jing, and Q. Zhang, “Finite-time H-control for a class of discrete-time switched singular timedelay systems subject to actuator saturation,” Appl. Math. Comput, vol. 261, pp. 264–283, 2015.MathSciNetMATHGoogle Scholar
  20. [20]
    R. A. Borges, R. C. L. F. Oliveir, C. T. Abdallah, and P. L. D. Peres, “H-filtering for discrete-time linear systems with bounded time varying parameters,” Signal Process., vol. 90, pp. 282–291, 2010. [click]CrossRefMATHGoogle Scholar
  21. [21]
    Q. Zhong, J. Cheng, Y. Zhao, J. Ma, and B. Huang, “Finitetime Hm filtering for a class of discrete-time Markovian jump systems with switching transition probabilities subject to average dwell time switching,” Appl. Math Comput., vol. 225, pp. 278–294, 2013. [click]MathSciNetMATHGoogle Scholar
  22. [22]
    L. A. Tuan and V. N. Phat, “Finite-time stability and H control of linear discrete-time delay systems with normbounded disturbances,” Acta Math. Vietnam., vol. 41, pp. 481–493, 2013.CrossRefMATHGoogle Scholar
  23. [23]
    Y. Ma, X. Jia, and D. Liu, “Robust finite-time HM control for discrete-time singular Markovian jump systems with time-varying delay,” Appl. Math Comput., vol. 286, pp. 213–227, 2016.MathSciNetGoogle Scholar
  24. [24]
    A. Liu, L. Yu, W. Zhang, and B. Chen, “H filtering for discrete-time genetic regulatory networks with random delays,” Math Biosci., vol. 239, pp. 97–105, 2012.MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    D. Zhang, L. Yu, Q. G. Wang, and C. J. Ong, Z. G. Wu, “Exponential H filtering for discrete-time switched singular systems with time-varying delays,” J.Frankin Inst., vol. 349, pp. 2323–2342, 2012.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    Y. Q. Zhang, C. X. Liu, and Y. D. Song, “Finite-time Hm filtering for discrete time markovian jump systems,” J.Frankn Inst., vol. 350, pp. 1579–1595, 2013.CrossRefMATHGoogle Scholar
  27. [27]
    W. Han, Y. Kao, and L. Wang, “Global exponential robust stability of static interval neural networks with S-type distributed delays,” J. Frankl. Inst., vol. 348, pp. 2072–2081, 2011.MathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    Q. Song and J. Cao, “Global robust stability of interval neural networks with multiple time-varying delays,” Math. Comput. Simul., vol.74, pp. 38–46, 2008.MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    Q. Song, “Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach,” Neurocomputing, vol. 71, pp. 2823–2830, 2008. [click]CrossRefGoogle 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 IT Information and Control EngineeringKunsan National UniversityKunsanKorea

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