Skip to main content
SpringerLink
Log in

Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper studies the stabilization problem of delayed memristive neural networks under event-triggered control. A refined switching event-trigger scheme that switches between variable sampling and continuous event-trigger can be designed by introducing an exponential decay term into the threshold function. Compared with the existing mechanisms, the proposed scheme can enlarge the interval between two successively triggered events and therefore can reduce the amount of triggering times. By constructing a time-dependent and piecewise-defined Lyapunov functional, a less-conservative criterion can be derived to ensure global stability of the closed-loop system. Based on matrix decomposition, equivalent conditions in linear matrix inequalities form of the above stability criterion can be established for the co-design of both the trigger matrix and the feedback gain. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and the advantages of the refined switching event-trigger scheme.

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

Similar content being viewed by others

References

  1. Chua L. Memristor-the missing circuit element. IEEE Trans Circ Theory, 1971, 18: 507–519

    Google Scholar 

  2. Wang L M, Shen Y. Design of controller on synchronization of memristor-based neural networks with time-varying delays. Neurocomputing, 2015, 147: 372–379

    Google Scholar 

  3. Yang X S, Ho D W C. Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern, 2016, 46: 3377–3387

    Google Scholar 

  4. Yang X S, Cao J D, Liang J L. Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst, 2017, 28: 1878–1888

    MathSciNet  Google Scholar 

  5. Fan Y J, Huang X, Li Y X, et al. Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: an interval matrix and matrix measure combined method. IEEE Trans Syst Man Cybern Syst, 2019, 49: 2254–2265

    Google Scholar 

  6. Li N, Cao J D. Lag synchronization of memristor-based coupled neural networks via ω-measure. IEEE Trans Neural Netw Learn Syst, 2016, 27: 686–697

    MathSciNet  Google Scholar 

  7. Liu H J, Wang Z D, Shen B, et al. Event-triggered H∞ state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case. IEEE Trans Neural Netw Learn Syst, 2018, 29: 3726–3737

    MathSciNet  Google Scholar 

  8. Cao J D, Li R X. Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci, 2017, 60: 032201

    Google Scholar 

  9. Jia J, Huang X, Li Y X, et al. Global stabilization of fractional-order memristor-based neural networks with time delay. 2019. doi: https://doi.org/10.1109/TNNLS.2019.2915353

  10. Choi H, Jung H, Lee J, et al. An electrically modifiable synapse array of resistive switching memory. Nanotechnology, 2009, 20: 345201

    Google Scholar 

  11. Kim H, Sah M P, Yang C J, et al. Neural synaptic weighting with a pulse-based memristor circuit. IEEE Trans Circ Syst I, 2012, 59: 148–158

    MathSciNet  MATH  Google Scholar 

  12. Liao X F, Yu J B. Robust stability for interval Hopfield neural networks with time delay. IEEE Trans Neural Netw, 1998, 9: 1042–1045

    Google Scholar 

  13. Wu A L, Zeng Z G. Exponential stabilization of memristive neural networks with time delays. IEEE Trans Neural Netw Learn Syst, 2012, 23: 1919–1929

    Google Scholar 

  14. Guo Z Y, Wang J, Yan Z. Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays. Neural Netw, 2013, 48: 158–172

    MATH  Google Scholar 

  15. Zhang G D, Shen Y. Exponential stabilization of memristor-based chaotic neural networks with time-varying delays via intermittent control. IEEE Trans Neural Netw Learn Syst, 2015, 26: 1431–1441

    MathSciNet  Google Scholar 

  16. Wen S P, Huang T W, Zeng Z G, et al. Circuit design and exponential stabilization of memristive neural networks. Neural Netw, 2015, 63: 48–56

    MATH  Google Scholar 

  17. Ding S B, Wang Z S, Rong N N, et al. Exponential stabilization of memristive neural networks via saturating sampleddata control. IEEE Trans Cybern, 2017, 47: 3027–3039

    Google Scholar 

  18. Zhang W, Branicky M S, Phillips S M. Stability of networked control systems. IEEE Control Syst, 2001, 21: 84–99

    Google Scholar 

  19. Ge X H, Yang F W, Han Q L. Distributed networked control systems: a brief overview. Inf Sci, 2017, 380: 117–131

    Google Scholar 

  20. Hespanha J P, Naghshtabrizi P, Xu Y G. A survey of recent results in networked control systems. Proc IEEE, 2007, 95: 138–162

    Google Scholar 

  21. Ogren P, Fiorelli E, Leonard N E. Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment. IEEE Trans Autom Control, 2004, 49: 1292–1302

    MathSciNet  MATH  Google Scholar 

  22. Walsh G C, Ye H. Scheduling of networked control systems. IEEE Control Syst, 2001, 21: 57–65

    Google Scholar 

  23. Tabuada P. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans Autom Control, 2007, 52: 1680–1685

    MathSciNet  MATH  Google Scholar 

  24. Borgers D P, Heemels W P M H. Event-separation properties of event-triggered control systems. IEEE Trans Autom Control, 2014, 59: 2644–2656

    MathSciNet  MATH  Google Scholar 

  25. Heemels W P M H, Donkers M C F, Teel A R. Periodic event-triggered control for linear systems. IEEE Trans Autom Control, 2013, 58: 847–861

    MathSciNet  MATH  Google Scholar 

  26. Zhang X M, Han Q L, Zhang B L. An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems. IEEE Trans Ind Inf, 2017, 13: 4–16

    Google Scholar 

  27. Lunze J, Lehmann D. A state-feedback approach to event-based control. Automatica, 2010, 46: 211–215

    MathSciNet  MATH  Google Scholar 

  28. Yue D, Tian E G, Han Q L. A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans Autom Control, 2013, 58: 475–481

    MathSciNet  MATH  Google Scholar 

  29. Wen S P, Zeng Z G, Chen M Z, et al. Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans Neural Netw Learn Syst, 2017, 28: 2334–2343

    MathSciNet  Google Scholar 

  30. Wang J, Chen M S, Shen H. Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model. Nonlinear Dyn, 2017, 87: 2741–2753

    MathSciNet  MATH  Google Scholar 

  31. Shen B, Wang Z D, Qiao H. Event-triggered state estimation for discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements. IEEE Trans Neural Netw Learn Syst, 2017, 28: 1152–1163

    Google Scholar 

  32. Duan G P, Xiao F, Wang L. Hybrid event- and time-triggered control for double-integrator heterogeneous networks. Sci China Inf Sci, 2019, 62: 022203

    MathSciNet  Google Scholar 

  33. Selivanov A, Fridman E. A switching approach to event-triggered control. In: Proceedings of the 54th IEEE Conference on Decision and Control, Osaka, 2015. 5468–5473

  34. Selivanov A, Fridman E. Event-triggered H∞ control: a switching approach. IEEE Trans Autom Control, 2016, 61: 3221–3226

    MathSciNet  Google Scholar 

  35. Fei Z Y, Guan C X, Gao H J. Exponential synchronization of networked chaotic delayed neural network by a hybrid event trigger scheme. IEEE Trans Neural Netw Learn Syst, 2018, 29: 2558–2567

    MathSciNet  Google Scholar 

  36. Fan Y J, Huang X, Shen H, et al. Switching event-triggered control for global stabilization of delayed memristive neural networks: an exponential attenuation scheme. Neural Netw, 2019, 117: 216–224

    MATH  Google Scholar 

  37. Filippov A F. Differential Equations with Discontinuous Righthand Sides. Boston: Kluwer, 1988

    Google Scholar 

  38. Aubin J P, Cellina A. Differential Inclusions. Berlin: Springer, 1984

    MATH  Google Scholar 

  39. Fridman E. A refined input delay approach to sampled-data control. Automatica, 2010, 46: 421–427

    MathSciNet  MATH  Google Scholar 

  40. Suh Y S. Stability and stabilization of nonuniform sampling systems. Automatica, 2008, 44: 3222–3226

    MathSciNet  MATH  Google Scholar 

  41. Seuret A, Gouaisbaut F. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 2013, 49: 2860–2866

    MathSciNet  MATH  Google Scholar 

  42. Zhou J P, Park J H, Ma Q. Non-fragile observer-based H∞ control for stochastic time-delay systems. Appl Math Comput, 2016, 291: 69–83

    MathSciNet  MATH  Google Scholar 

  43. Boyd S, El Ghaoui L, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61973199, 61473178, 61573008). We would thank anonymous reviewers for their valuable suggestions.

Author information

Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhilian Yan & Xia Huang

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

Authors
  1. Zhilian Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xia Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xia Huang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, Z., Huang, X. & Cao, J. Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control. Sci. China Inf. Sci. 63, 212201 (2020). https://doi.org/10.1007/s11432-019-2664-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-019-2664-7

Keywords

Search

Navigation