Event-triggered Non-fragile State Estimation for Discrete Nonlinear Markov Jump Neural Networks with Sensor Failures

  • Jianning LiEmail author
  • Zhujian Li
  • Yufei Xu
  • Kaiyang Gu
  • Wendong Bao
  • Xiaobin Xu


This paper investigates the non-fragile state estimation problem for discrete nonlinear Markov jump neural networks(MJNNs) with sensor failures. Due to the limit communication resource, we adopt a kind of event-triggered mechanism to determine whether the sensor sampling information is sent or not. By selecting suitable Lyapunov functions, a sufficient condition is obtained to guarantee the mean-square exponential stability of the augmented system. Finally, a numerical example is given to show the effectiveness of the proposed method.


Event-trigger mechanism Markov jump neural networks non-fragile state estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Arik, “Global asymptotic stability of a class of dynamical neural networks,” IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications, vol. 47, No. 4, pp. 4–568, 2000.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Y. Fu and T. Chai, “Nonlinear adaptive decoupling control based on neural networks and multiple models,” International Journal of Innovative Computing, Information and Control, vol. 8, No. 3, pp. 3–1867, 2012.Google Scholar
  3. [3]
    Y. He, M. Wu, J. H. She, and G.-P. Liu, “Delay-dependent robust stability criteria for uncertain neural systems with mixed delays,” Systems & Control Letters, vol. 51, No. 1, pp. 1–57, 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Li and L. Li, “Mean-square exponential stability for stochastic discrete-time recurrent neural networks with mixed time delays,” Neurocomputing, vol. 151, pp. 790–797, 2015.CrossRefGoogle Scholar
  5. [5]
    J.-N. Li, W.-D. Bao, S.-B. Li, C.-L. Wen, and L.-S. Li, “Exponential synchronization of discrete-time mixed delay neural networks with actuator constraints and stochastic missing data,” Neurocomputing, vol. 207, pp. 700–707, 2016.CrossRefGoogle Scholar
  6. [6]
    Z.-G. Wu, J. H. Park, H. Su, and J. Chu, “Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates,” Nonlinear Analysis Real World Applications, vol. 13, No. 5, pp. 5–2423, 2012.MathSciNetzbMATHGoogle Scholar
  7. [7]
    H. Shen, Y. Zhu, L. Zhang, and J. H. Park, “Extended dis-sipative state estimation for Markov jump neural networks with unreliable links,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, No. 2, pp. 2–346, 2017.CrossRefGoogle Scholar
  8. [8]
    Z. Wu, H. Su, and J. Chu, “State estimation for discrete Markovian jumping neural networks with time delay,” Neurocomputing, vol. 73, pp. 2247–2254, 2010.CrossRefGoogle Scholar
  9. [9]
    J.-N. Li, Y.-F. Xu, K.-Y Gu, L.-S. Li, and X.-B. Xu, “Mixed passive/H∞ hybrid control for delayed Markovian jump system with actuator constraints and fault alarm,” International Journal of Robust and Nonlinear Control, vol. 28, No. 18, pp. 18–6016, 2018.MathSciNetzbMATHGoogle Scholar
  10. [10]
    G. H. Yang and J. L. Wang, “Non-fragile H∞ control for linear systems with multiplicative controller gain variations,” Automatica, vol. 37, No. 1, pp. 1–1727, 2001.MathSciNetCrossRefGoogle Scholar
  11. [11]
    H. P. Du, J. Lam, and K. Y. Sze, “Non-fragile output feedback ft. vehicle suspension control using genetic algorithm,” Engineering Applications of Artificial Intelligence, vol. 16, no.7, pp. 667–680, 2003.CrossRefGoogle Scholar
  12. [12]
    Z. Li, Z. Wang, D. Ding, and H. Shu, “Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings,” IET Control Theory and Applications, vol. 9, No. 2, pp. 2–222, 2015.MathSciNetCrossRefGoogle Scholar
  13. [13]
    J.-N. Li, Y.-F. Xu, W.-D. Bao, Z.-J. Li, and L.-S. Li, “Finite-time non-fragile state estimation for discrete neural networks with sensor failures time-varying delays and randomly occurring sensor nonlinearity,” Journal of the Franklin Institute, vol. 356, No. 3, pp. 3–1566, 2019.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Z. Wang, Y. Liu, and X. Liu, “On global asymptotic stability of neural networks with discrete and distributed delays,” Physics Letters A, vol. 345, No. 4, pp. 4–299, 2005.Google Scholar
  15. [15]
    R. Habtom and L. Litz, “Estimation of unmeasured inputs using recurrent neural networks and the extended Kalman filter,” Proc. of International Conference on Neural Networks, IEEE, pp.2067–2071, 1997.CrossRefGoogle Scholar
  16. [16]
    T. Wang, H. Gao, and J. Qiu, “A combined adaptive neural network and nonlinear model predictive control for multi-rate networked industrial process control,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, No. 2, pp. 2–416, 2016.CrossRefGoogle Scholar
  17. [17]
    H. Li, B. Chen, Q. Zhou, and S. Fang, “Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays,” Physics Letters A, vol. 372, No. 19, pp. 19–3385, 2008.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    L. Zhang, H. Gao, and O. Kaynak, “Network-induced constraints in networked control systems survey,” IEEE Trans. Ind. Inf., vol. 9, No. 1, pp. 1–403, 2012.Google Scholar
  19. [19]
    L. Hetel, C. Fiter, H. Omran, A. Seuret, E. Fridman, J. P. Richard, and S. I. Niculescu, “Recent developments on the stability of systems with aperiodic sampling: an overview,” Automatica, vol. 76, pp. 309–335, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    P. Tabuada, “Event-triggered real-time scheduling of stabilizing control tasks,” IEEE Trans. Autom. Control, vol. 52, No. 9, pp. 9–1680, 2007.MathSciNetzbMATHGoogle Scholar
  21. [21]
    D. Zhang, Q. L. Han, and X. Jia, “Network-based output tracking control for T-S fuzzy systems using an event-triggered communication scheme,” Fuzzy Sets Syst., vol. 273, pp. 26–48, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    C. Peng, S. Ma, and X. Xie, “Observer-based Non-PDC control for networked T-S fuzzy systems with an event-triggered communication,” IEEE Trans. Cybern., vol. 47, No. 8, pp. 8–2279, 2017.Google Scholar
  23. [23]
    X. M. Zhang, Q. L. Han, and B. L. Zhang, “An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems,” IEEE Trans. Ind. Inf., vol. 13, No. 1, pp. 1–4, 2017.MathSciNetCrossRefGoogle Scholar
  24. [24]
    J. Lunze and D. Lehmann, “A state-feedback approach to event-based control,” Automatica, vol. 46, No. 1, pp. 1–211, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    A. Eqtami, D. V. Dimarogonas, and K. J. Kyriakopou-los, “Event-triggered control for discrete-time systems,” Proc. of American Control Conference, IEEE, pp.4719–4724, 2010.Google Scholar
  26. [26]
    S. Hu and D. Yue, “Event-based H∞ filtering for networked system with communication delay,” Signal Processing, vol. 92, No. 9, pp. 9–2029, 2012.CrossRefGoogle Scholar
  27. [27]
    H. Ren, G. Zong, and T. Li, “Event-triggered finite-time control for networked switched linear systems with asynchronous switching,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, pp. 1–11, 2018.Google Scholar
  28. [28]
    H. Ren, G. Zong, and H. R. Karimi, “Asynchronous finite-time filtering of networked switched systems and its application: an event-driven method,” IEEE Transactions on Circuits and Systems I: Regular Papers, pp. 1–12, 2018.Google Scholar
  29. [29]
    L. Zha, J. Fang, J. Liu, and E. Tian, “Event-triggered non-fragile state estimation for delayed neural networks with randomly occurring sensor nonlinearity,” Neurocomputing, vol. 273, pp. 1–8, 2018.CrossRefGoogle Scholar
  30. [30]
    H. Sun, Y. Li, G. Zong, and L. Hou, “Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities,” Automatica, vol. 89, pp. 349–357, 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    G. Zong, D. Yang, L. Hou, and Q. Wang, “Robust finite-time H∞ control for Markovian jump systems with partially known transition probabilities,” Journal of the Franklin Institute, vol. 350, No. 6, pp. 6–1562, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    Z. Gao and H. Wang, “Descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis,” Systems & Control Letters, vol. 55, No. 4, pp. 4–304, 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    Z. Gao and D. W. C. Ho, “State/noise estimator for descriptor systems with application to sensor fault diagnosis,” IEEE Transactions on Signal Processing, vol. 54, No. 4, pp. 4–1316, 2006.zbMATHGoogle Scholar
  34. [34]
    X. Wang and G. Yang, “Event-triggered fault detection for discrete-time T-S fuzzy systems,” ISA Transactions, vol. 76, pp. 18–30, 2018.CrossRefGoogle Scholar
  35. [35]
    S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadelphia, 1994.CrossRefzbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Jianning Li
    • 1
    Email author
  • Zhujian Li
    • 1
  • Yufei Xu
    • 1
  • Kaiyang Gu
    • 1
  • Wendong Bao
    • 1
  • Xiaobin Xu
    • 1
  1. 1.Institute of System Science and Control Engineering, School of AutomationHangzhou Dianzi UniversityHangzhouP. R. China

Personalised recommendations