Skip to main content

Advertisement

SpringerLink
Log in

Global Dissipativity of Inertial Neural Networks with Proportional Delay via New Generalized Halanay Inequalities

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This article is devoted to the global dissipativity of inertial neural networks with proportional delay. A novel generalized Halanay inequality which involves proportional delay is established. By constructing a new generalized Halanay inequality, several new explicit delay-independent conditions are derived in terms of linear matrix inequalities to ensure the global dissipativity of the considered system. Moreover, a new differential delay inequality which involves unbounded time-varying delay is considered. Due to the proportional delay is one type of unbounded time-varying delays, new analysis techniques can effectively avoid the difficulties caused by proportional delay by applying a new differential delay inequality. Especially, several novel delay-dependent sufficient conditions are obtained to guarantee the global dissipativity of the considered system. Finally, two simulations examples are provided to illustrate the validity of the proposed 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

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
Fig. 4

Similar content being viewed by others

References

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

    Article  Google Scholar 

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

    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. Wen S, Zeng Z, Huang T, Meng Q (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26:1493–1502

    Article  MathSciNet  Google Scholar 

  5. Huang T, Li C, Duan S, Starzyk J (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 23(1–3):464–469

    Article  Google Scholar 

  7. Yang X, Ho D (2016) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern 46(12):3377–3387

    Article  Google Scholar 

  8. He X, Li C, Huang T, Li C, Huang J (2014) A recurrent neural network for solving bilevel linear programming problem. IEEE Trans Neural Netw Learn Syst 25:824–830

    Article  Google Scholar 

  9. Yang X, Cao J, Liang J (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 28(8):1878–1888

    Article  MathSciNet  Google Scholar 

  10. Zeng Z, Huang T, Zheng W (2010) Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Trans Neural Netw Learn Syst 21:1371–1377

    Article  Google Scholar 

  11. Huang H, Huang T, Chen X (2013) A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Netw 46:50–61

    Article  Google Scholar 

  12. Li C, Li C, Liao X, Huang T (2011) Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 74:1541–1550

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. 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 

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

    Article  Google Scholar 

  16. Feng Y, Li C, Huang T (2016) Periodically multiple state-jumps impulsive control systems with impulse time windows. Neurocomputing 193:7–13

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. 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 

  21. 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 

  22. 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 

  23. Hu J, Cao J, Alofi A, Abdullah AM, Elaiw A (2015) Pinning synchronization of coupled inertial delayed neural networks. Cogn Neurodyn 9(3):341–350

    Article  Google Scholar 

  24. Song Q, Cao J (2008) Global dissipativity analysis on uncertain neural networks with mixed time-varying delays. Chaos Interdiscip J Nonlinear Sci 18(4):043126

    Article  MathSciNet  Google Scholar 

  25. Song Q (2011) Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays. Neurocomputing 74(5):838–845

    Article  Google Scholar 

  26. Feng Y, Peng Y, Zou L, Tu Z, Liu J (2017) A note on impulsive control of nonlinear systems with impulse time window. J Nonlinear Sci Appl 10:3087–3098

    Article  MathSciNet  Google Scholar 

  27. Tu Z, Jian J, Wang B (2011) Positive invariant sets and global exponential attractive sets of a class of neural networks with unbounded time-delays. Commun Nonlinear Sci Numer Simul 16(9):3738–3745

    Article  MathSciNet  Google Scholar 

  28. Lu B, Jiang H, Abdurahman A, Hu C (2016) Global generalized exponential stability for a class of nonautonomous cellular neural networks via generalized Halanay inequalities. Neurocomputing 214:1046–1052

    Article  Google Scholar 

  29. 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 

  30. Song Q, Zhao Z (2005) Global dissipativity of neural networks with both variable and unbounded delays. Chaos Solitons Fractals 25(2):393–401

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161:99–106

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  34. Zheng C, Li N, Cao J (2015) Matrix measure based stability criteria for high-order neural networks with proportional delay. Neurocomputing 149:1149–1154

    Article  Google Scholar 

  35. 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 

  36. Zhou L (2014) Global asymptotic stability of cellular neural networks with proportional delays. Nonlinear Dyn 77(1–2):41–47

    Article  MathSciNet  Google Scholar 

  37. Liao X, Wang J (2003) Global dissipativity of continuous-time recurrent neural networks with time delay. Phys Rev E Stat Nonlinear Soft Matter Phys 68(2):016–118

    MathSciNet  Google Scholar 

  38. Wen L, Yu Y, Wang W (2008) Generalized Halanay inequalities for dissipativity of Volterra functional differential equations. J Math Anal Appl 347(1):169–178

    Article  MathSciNet  Google Scholar 

  39. Lu H (2002) Chaotic attractors in delayed neural networks. Phys Lett A 298(2–3):109–116

    Article  Google Scholar 

  40. Long S, Wang X, Li D (2012) Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays. Math Comput Simul 82(11):2199–2214

    Article  MathSciNet  Google Scholar 

  41. Feng Z, Lam J (2011) Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Trans Neural Netw 22(6):976–981

    Article  Google Scholar 

  42. Wu Z, Park J, Su H, Chu J (2012) Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties. Nonlinear Dyn 69(3):1323–1332

    Article  MathSciNet  Google Scholar 

  43. Zhou L (2013) Dissipativity of a class of cellular neural networks with proportional delays. Nonlinear Dyn 73(3):1895–1903

    Article  MathSciNet  Google Scholar 

  44. Hien L, Son D, Trinh H (2016) On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2016.2614998

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of People’s Republic of China (Grants Nos. 61633011, 61703346, 61374078),Graduate Student Research Innovation Project of Chongqing (Projet No. CYB17076), Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2015jcyjBX0052).

Author information

Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Hongfei Li, Chuandong Li & Wei Zhang

  2. College of Computer and Information Engineering, Xinjiang Agricultural University, Ürümqi, 830052, Xinjiang, People’s Republic of China

    Jing Xu

Authors
  1. Hongfei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuandong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jing Xu
    View author publications

    You can also search for this author in PubMed 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., Li, C., Zhang, W. et al. Global Dissipativity of Inertial Neural Networks with Proportional Delay via New Generalized Halanay Inequalities. Neural Process Lett 48, 1543–1561 (2018). https://doi.org/10.1007/s11063-018-9788-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9788-6

Keywords

Search

Navigation