Neural Computing and Applications

, Volume 31, Issue 1, pp 65–78 | Cite as

On passivity and robust passivity for discrete-time stochastic neural networks with randomly occurring mixed time delays

  • Jiahui Li
  • Hongli DongEmail author
  • Zidong Wang
  • Nan Hou
  • Fuad E. Alsaadi
Original Article


In this paper, the passivity analysis problem is investigated for a class of discrete-time stochastic neural networks (DSNNs) with randomly occurring mixed time delays (ROMDs). The mixed delays comprise time-varying discrete delays, infinite-distributed delays as well as finite-distributed delays. A set of Bernoulli-distributed white sequences is used to account for the random nature of the occurrence of the mixed time delays. In addition, stochastic disturbances are taken into consideration to describe the state-dependent noises caused possibly by electronic devices and hardware implementation of neural networks. By using a combination of Lyapunov-Krasovskii functional, free-weighting matrix approach and stochastic analysis technique, we establish sufficient conditions guaranteeing the passivity performance of the underlying DSNNs. Furthermore, a delay-dependent robust passivity criterion is presented to deal with the parameter uncertainties in the DSNNs with ROMDs. A simulation example is provided to verify the effectiveness of the proposed approach.


Discrete-time neural networks Stochastic neural networks Mixed time delays Randomly occurring time delays Robust passivity 



This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61422301 and 61374127, the Northeast Petroleum University Youth Top-Notch Talent Project RC201601, the Northeast Petroleum University Innovation Foundation for Postgraduate YJSCX2016-026NEPU and the Alexander von Humboldt Foundation of Germany.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Arik S (2014) An improved robust stability result for uncertain neural networks with multiple time delays. Neural Netw 54:1–10CrossRefzbMATHGoogle Scholar
  2. 2.
    Arik S (2014) New criteria for global robust stability of delayed neural networks with norm-bounded uncertainties. IEEE Trans Neural Netw Learn Syst 25(6):1045–1052CrossRefGoogle Scholar
  3. 3.
    Balasubramaniam P, Nagamani G (2012) Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays. Exp Syst Appl 39(1):732–742CrossRefGoogle Scholar
  4. 4.
    Boyd S, Ghaoui L E, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  5. 5.
    Chen B, Li H, Lin C, Zhou Q (2009) Passivity analysis for uncertain neural networks with discrete and distributed time varying delays. Phys Lett A 373(14):1242–1248MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chen H, Liang J, Wang Z (2016) Pinning controllability of autonomous Boolean control networks. Sci China Inf Sci 59(7):Art. No. 070107. doi: 10.1007/s11432-016-5579-8 CrossRefGoogle Scholar
  7. 7.
    Gao H, Chen T, Chai T (2007) Passivity and passification for networked control systems. SIAM J Control Optim 46(4):1299–1322MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hu S, Wang J (2002) Global stability of a class of discrete-time recurrent neural networks. IEEE Trans Circ Syst I 49(8):1104–1117MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Li C, Liao X (2005) Passivity analysis of neural networks with time delay. IEEE Trans Circuits Syst Express Briefs 52(8):471–475MathSciNetCrossRefGoogle Scholar
  10. 10.
    Li H, Wang C, Shi P, Gao H (2010) New pssivity results for uncertain discrete-time stochastic neural networks with mixed time delays. Neurocomputing 73(4–6):3291–3299CrossRefGoogle Scholar
  11. 11.
    Li Q, Shen B, Liu Y, Alsaadi F E (2016) Event-triggered \(H_{\infty }\) state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays. Neurocomputing 174:912–920CrossRefGoogle Scholar
  12. 12.
    Li R, Cao J, Tu Z (2016) Passivity analysis of memristive neural networks with probabilistic time-varying delays. Neurocomputing 191:249–262CrossRefGoogle Scholar
  13. 13.
    Li W, Wei G, Han F, Liu Y (2016) Weighted average consensus-based unscented Kalman filtering. IEEE Trans Cybern 46(2):558–567CrossRefGoogle Scholar
  14. 14.
    Liu D, Liu Y, Alsaadi F E (2016) A new framework for output feedback controller design for a class of discrete-time stochastic nonlinear system with quantization and missing measurement. Int J Gen Syst 45(5):517–531MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Liu S, Wei G, Song Y, Liu Y (2016) Extended Kalman filtering for stochastic nonlinear systems with randomly occurring cyber attacks. Neurocomputing 207:708–716CrossRefGoogle Scholar
  16. 16.
    Liu Y, Liu W, Obaid M A, Abbas I A (2016) Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays. Neurocomputing 177:409–415CrossRefGoogle Scholar
  17. 17.
    Liu Y, Wang Z, Liang J, Liu X (2008) Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans Syst Man Cybern B 38(5):1314–1325CrossRefGoogle Scholar
  18. 18.
    Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675CrossRefzbMATHGoogle Scholar
  19. 19.
    Liu Y, Wang Z, Serrano A, Liu X (2006) Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis. Phys Lett A 362(5-6):480–488CrossRefGoogle Scholar
  20. 20.
    Lou X, Cui B (2007) Passivity analysis of integro-differential neural networks with time-varying delays. Neurocomputing 70(4–6):1071–1078CrossRefGoogle Scholar
  21. 21.
    Sheng L, Wang Z, Tian E, Alsaadi F E (2016) Delay-distribution-dependent \(H_{\infty }\) state estimation for delayed neural networks with (x,v)-dependent noises and fading channels. Neural Netw 84:102–112CrossRefGoogle Scholar
  22. 22.
    Shu H, Zhang S, Shen B, Liu Y (2016) Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises. Int J Gen Syst 45(5):648– 661MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Song Q, Liang J, Wang Z (2009) Passivity analysis of discrete-time stochastic neural networks with time-varying delays. Neurocomputing 72(7–9):1782–1788CrossRefGoogle Scholar
  24. 24.
    Song Q, Wang Z (2007) A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays. Phys Lett A 368:134–145CrossRefGoogle Scholar
  25. 25.
    Song Q, Zhang J (2008) Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays. Nonlinear Anal: Real World Appl 9:500–510MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Thuan M V, Trinh H, Hien L V (2016) New inequality-based approach to passivity analysis of neural networks with interval time-varying delay. Neurocomputing 194:301–307CrossRefGoogle Scholar
  27. 27.
    Wang L, Xu Z (2006) Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks. IEEE Trans Circuits Syst I 53(6):1373–1380MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Wen C, Cai Y, Liu Y, Wen C (2016) A reduced-order approach to filtering for systems with linear equality constraints. Neurocomputing 193:219–226CrossRefGoogle Scholar
  29. 29.
    Wu L, Zheng W (2009) Passivity-based sliding mode control of uncertain singular time-delay systems. Automatica 45(9):2120–2127MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Wu Z, Shi P, Su H, Chu J (2011) Delay-dependent stability analysis for switched neural networks with time-varying delay. IEEE Trans Syst Man Cybern B Cybern 41(6):1522– 1530CrossRefGoogle Scholar
  31. 31.
    Yu W (2003) Passivity analysis for dynamic multilayer neuro identifier. IEEE Trans Circuits Syst I 50 (1):173–178MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Yue D, Zhang Y, Tian E, Peng C (2008) Delay-distribution-dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delay. IEEE Trans Neural Netw 19(7):1299–1306CrossRefGoogle Scholar
  33. 33.
    Zeng H, He Y, Wu M, Xiao H (2014) Improved conditions for passivity of neural networks with a time-varying delay. IEEE Tran Cybern 44(6):785–792CrossRefGoogle Scholar
  34. 34.
    Zeng H, He Y, Wu M, Xiao S (2011) Passivity analysis for neural networks with a time-varying delay. Neurocomputing 74(5):730–734CrossRefGoogle Scholar
  35. 35.
    Zeng J, Park H, Shen H (2015) Robust passivity analysis of neural networks with discrete and distributed delays. Neurocomputing 149:1092–1097CrossRefGoogle Scholar
  36. 36.
    Zeng N, Wang Z, Zhang H (2016) Inferring nonlinear lateral flow immunoassay state-space models via an unscented Kalman filter. Sci China Inf Sci 59(11):Art. No. 112204. doi: 10.1007/s11432-016-0280-9 CrossRefGoogle Scholar
  37. 37.
    Zhang J, Ma L, Liu Y (2016) Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects. Neurocomputing 216:657–665CrossRefGoogle Scholar
  38. 38.
    Zhang Y, Xu S, Chu Y, Lu J (2010) Robust global synchronization of complex networks with neutral-type delayed nodes. Appl Math Comput 216(3):768–778MathSciNetzbMATHGoogle Scholar
  39. 39.
    Zhang W, Wang Z, Liu Y, Ding D, Alsaadi F E (2017) Event-based state estimation for a class of complex networks with time-varying delays: a comparison principle approach. Phys Lett A 381(1): 10–18MathSciNetCrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Jiahui Li
    • 1
    • 2
  • Hongli Dong
    • 1
    • 2
    Email author
  • Zidong Wang
    • 3
    • 4
  • Nan Hou
    • 1
    • 2
  • Fuad E. Alsaadi
    • 4
  1. 1.Institute of Complex Systems and Advanced ControlNortheast Petroleum UniversityDaqingChina
  2. 2.Heilongjiang Provincial Key Laboratory of Networking and Intelligent ControlNortheast Petroleum UniversityDaqingChina
  3. 3.Department of Computer ScienceBrunel University LondonUxbridgeUK
  4. 4.Communication Systems and Networks (CSN) Research Group, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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