Skip to main content
Springer Nature Link
Log in

Global asymptotical stability for a class of non-autonomous impulsive inertial neural networks with unbounded time-varying delay

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This article is concerned with the global asymptotical stability of non-autonomous impulsive inertial neural networks with unbounded delay. A new impulsive differential delay inequality which involves unbounded and non-differential delay is established. Moreover, based on a new impulsive differential delay inequality, new analysis techniques can effectively avoid the difficulties caused by unbounded delay and impulses, and several novel delay-dependent inequalities are obtained to ensure the global stability of this model. In the end, three examples are given to claim the validity of theoretical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Zhang P, Li C, Huang T, Chen L, Chen Y (2017a) Forgetting memristor based neuromorphic system for pattern training and recognition. Neurocomputing 222:47–53

    Article  Google Scholar 

  2. Li C, Yu X, Huang T, He X (2017a) Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch. IEEE Trans Neural Netw Learning Syst. https://doi.org/10.1109/TNNLS.2017.2691760

    Article  Google Scholar 

  3. Li H, Jiang H, Hu C (2016) Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays. Neural Netw 75:97–109

    Article  Google Scholar 

  4. He X, Ho DW, Huang T, Yu J, Abu-Rub H, Li C (2017a) Second-order continuous-time algorithms for economic power dispatch in smart grids. IEEE Trans Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2017.2672205

    Article  Google Scholar 

  5. Huang T, Li C, Duan S, Starzyk JA (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23(6):866–875

    Article  Google Scholar 

  6. Babcock K, Westervelt R (1986) Stability and dynamics of simple electronic neural networks with added inertia. Phys D Nonlinear Phenom 23(1–3):464–469

    Article  Google Scholar 

  7. Liu B, Lu W, Chen T (2013) Pinning consensus in networks of multiagents via a single impulsive controller. IEEE Trans Neural Netw Learn Syst 24(7):1141–1149

    Article  Google Scholar 

  8. Qi J, Li C, Huang T (2015) Stability of inertial BAM neural network with time-varying delay via impulsive control. Neurocomputing 161:162–167

    Article  Google Scholar 

  9. Zhou L, Zhang Y (2016) Global exponential stability of a class of impulsive recurrent neural networks with proportional delays via fixed point theory. J Frankl Inst 353(2):561–575

    Article  MathSciNet  Google Scholar 

  10. Li X, Song S (2013) Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learn Syst 24(6):868–877

    Article  Google Scholar 

  11. Aouiti C, M’hamdi MS, Touati A (2017) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121–140

    Article  Google Scholar 

  12. Song X, Zhao P, Xing Z, Peng J (2016) Global asymptotic stability of cnns with impulses and multi-proportional delays. Math Methods Appl Sci 39(4):722–733

    Article  MathSciNet  Google Scholar 

  13. Aouiti C (2016a) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn 10(6):573–591

    Article  MathSciNet  Google Scholar 

  14. Yang X, Cao J, Yang Z (2013) Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM J Control Optim 51(5):3486–3510

    Article  MathSciNet  Google Scholar 

  15. Guan Z, Chen G (1999) On delayed impulsive Hopfield neural networks. Neural Netw 12(2):273–280

    Article  Google Scholar 

  16. Aouiti C (2016b) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2558-3

    Article  Google Scholar 

  17. Li X, Rakkiyappan R (2013) Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays. Commun Nonlinear Sci Numer Simul 18(6):1515–1523

    Article  MathSciNet  Google Scholar 

  18. Wan P, Jian J (2017) Global convergence analysis of impulsive inertial neural networks with time-varying delays. Neurocomputing 245:68–76

    Article  Google Scholar 

  19. Tu Z, Cao J, Alsaedi A, Alsaadi F (2017) Global dissipativity of memristor-based neutral type inertial neural networks. Neural Netw 88:125–133

    Article  Google Scholar 

  20. Li H, Li C, Huang T (2017b) Periodicity and stability for variable-time impulsive neural networks. Neural Netw 94:24–33

    Article  Google Scholar 

  21. Li X, Zhang X, Song S (2017c) Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica 76:378–382

    Article  MathSciNet  Google Scholar 

  22. Wheeler D, Schieve W (1997) Stability and chaos in an inertial two-neuron system. Phys D Nonlinear Phenom 105(4):267–284

    Article  Google Scholar 

  23. Mauro A, Conti F, Dodge F, Schor R (1970) Subthreshold behavior and phenomenological impedance of the squid giant axon. J Gen Physiol 55(4):497–523

    Article  Google Scholar 

  24. He X, Huang T, Yu J, Li C, Li C (2017b) An inertial projection neural network for solving variational inequalities. IEEE Trans Cybern 47(3):809–814

    Article  Google Scholar 

  25. Zhang W, Huang T, He X, Li C (2017) Global exponential stability of inertial memristor-based neural networks with time-varying delayed and impulses. Neural Netw. https://doi.org/10.1016/j.neunet.2017.03.012

    Article  Google Scholar 

  26. Tu Z, Cao J, Hayat T (2016) Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks. Neural Netw 75:47–55

    Article  Google Scholar 

  27. Esteves S, Oliveira J (2015) Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays. Appl Math Comput 265:333–346

    MathSciNet  MATH  Google Scholar 

  28. Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355

    Article  Google Scholar 

  29. Zhao Z, Song Q, Zhang J (2006) Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays. Comput Math Appl 51(3–4):475–486

    Article  MathSciNet  Google Scholar 

  30. Ammar B, Chrif F, Alimi A (2012) Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. IEEE Trans Neural Netw Learn Syst 23(1):109–118

    Article  Google Scholar 

  31. Zhang A (2017) Almost periodic solutions for SICNNs with neutral type proportional delays and D, operators. Neural Process Let 6:1–14

    Google Scholar 

  32. Bemporad A (1998) Predictive control of teleoperated constrained systems with unbounded communication delays. Proc IEEE Conf Decis Control 2:2133–2138

    Google Scholar 

  33. Zeng Z, Wang J, Liao X (2005) Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays. IEEE Trans Circuits Syst 52–II(3):168–173

    Article  Google Scholar 

  34. Koo M, Choi H, Lim J (2012) Output feedback regulation of a chain of integrators with an unbounded time-varying delay in the input. IEEE Trans Automat Contr 57(10):2662–2667

    Article  MathSciNet  Google Scholar 

  35. Liu B, Lu W, Chen T (2011) Generalized Halanay inequalities and their applications to neural networks with unbounded time-varying delays. IEEE Trans Neural Netw 22(9):1508–1513

    Article  Google Scholar 

  36. Chen T, Liu X (2017) \(\mu\)-stability of nonlinear positive systems with unbounded time-varying delays. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2016.2533392

    Article  MathSciNet  Google Scholar 

  37. Li X, Cao J (2017) An impulsive delay inequality involving unbounded time-varying delay and applications. IEEE Trans Automat Contr. https://doi.org/10.1109/TAC.2017.2669580

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of People’s Republic of China (Grant Nos. 61633011,61703346, 61374078), Graduate Student Research Innovation Project of Chongqing (Projet No. CYB17076).

Author information

Authors and Affiliations

  1. National and Local Joint Engineering Laboratory of Intelligent Transmission and Control Technology (Chongqing), College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Hongfei Li, Wei Zhang, Chuandong Li & Wanli Zhang

Authors
  1. Hongfei Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Wei Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Chuandong Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Wanli Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Chuandong Li.

Ethics declarations

Conflicts of interest

The authors declare that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, H., Zhang, W., Li, C. et al. Global asymptotical stability for a class of non-autonomous impulsive inertial neural networks with unbounded time-varying delay. Neural Comput & Applic 31, 6757–6766 (2019). https://doi.org/10.1007/s00521-018-3498-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-018-3498-x

Keywords