Skip to main content
SpringerLink
Log in

New Criteria on Exponential Lag Synchronization of Switched Neural Networks with Time-Varying Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper addresses the problem of global exponential lag synchronization of switched neural networks with time-varying delays and general activation functions. Based on the Lyapunov–Krasovskii functional method and free weighting matrix technique, delay-dependent criteria for the global exponential lag synchronization of switched neural networks are derived in form of linear matrix inequalities. A numerical example is utilized to illustrate the characteristics of the results.

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

Similar content being viewed by others

References

  1. Huang H, Qu Y, Li H (2005) Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys Lett A 345:345–354

    Article  MATH  Google Scholar 

  2. Huang H, Feng G (2009) Synchronization of nonidentical chaotic neural networks with time delays. Neural Netw 22:869–874

    Article  MATH  Google Scholar 

  3. He X, Li CD, Huang TW, Li CJ (2013) Codimension two bifurcation in a delayed neural network with unidirectional coupling. Nonlinear Anal RWA 14:1191–1202

    Article  MathSciNet  MATH  Google Scholar 

  4. He X, Li CD, Huang TW (2014) A Recurrent Neural Network for Solving Bilevel Linear Programming Problem. IEEE Trans Neural Netw Learn Syst 25(4):824–830

    Article  Google Scholar 

  5. Yang X, Cao J, Liang J (2016) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2561298

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

    Article  MATH  Google Scholar 

  7. Guo Z, Yang S, Wang J (2015) Global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling. IEEE Trans Neural Netw Learn Syst 26(6):1300–1311

    Article  MathSciNet  Google Scholar 

  8. Guo Z, Wang J, Yan Z (2015) Global exponential synchronization of two memristor-based recurrent neural networks with time delays via static or dynamic coupling. IEEE Trans Syst Man Cybern Syst 45(2):235–249

    Article  Google Scholar 

  9. Guo Z, Wang J, Yan Z (2014) Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25(4):704–717

    Article  Google Scholar 

  10. Zhou L (2015) Delay-dependent exponential synchronization of recurrent neural networks with multiple proportional delays. Neural Process Lett 42(3):619–632

    Article  Google Scholar 

  11. Wang X, Li C, Huang T, Duan S (2013) Global exponential stability of a class of memristive neural networks with time-varying delays. Neural Comput Appl. doi:10.1007/s00521-013-1383-1

    Google Scholar 

  12. Chen L, Li C, Huang T, Chen Y, Wang X (2013) Memristor crossbar-based unsupervised image learning. Neural Comput Appl. doi:10.1007/s00521-013-1501-0

  13. Shen Y, Miao P, Huang Y et al (2015) Finite-time stability and its application for solving time-varying Sylvester equation by recurrent neural networks. Neural Process Lett 42(3):763–784

    Article  Google Scholar 

  14. Li H, Liao X, Huang T, Wang Y, Han Q, Dong T (2014) Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies. Inform Sci 259:25–35

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhou B, Liao X, Huang T, Wang H, Chen G (2015) Constrained consensus of asynchronous discrete-time multi-agent systems with time-varying topology. Inform Sci 320:223–234

    Article  MathSciNet  Google Scholar 

  16. Wang H, Liao X, Huang T, Chen G (2015) Distributed parameter estimation in unreliable WSNs: Quantized communication and asynchronous intermittent observation. Inform Sci 309:11–25

    Article  MathSciNet  Google Scholar 

  17. Yang X, Cao J, Qiu J (2015) \(p_{th}\) moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91

    Article  Google Scholar 

  18. Chua L, Roska T (2002) Cellular networks and visual computing: foundations and applications. Cambridge University Press, Cambbridge

    Book  Google Scholar 

  19. Chen G, Dong X (1998) From chaos to order: methodolgies, perspectives, and applications. World Scientific, Singapore

    Book  Google Scholar 

  20. Zhang HG, Ma TD, Huang GB, Wang ZL (2010) Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Trans Syst Man Cybern B Cybern 40:831–844

    Article  Google Scholar 

  21. Liang JL, Wang ZD, Liu YR, Li XH (2008) Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans Syst Man Cybern B Cybern 38:1073–1083

    Article  Google Scholar 

  22. Wen S, Zeng Z, Huang T (2013) Passivity analysis of memristor-based recurrent neural networks with time-varying delays. J Frankl Inst 350:2354–2370

    Article  MathSciNet  MATH  Google Scholar 

  23. Cao JD, Chen GR, Li P (2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans Syst Man Cybern B Cybern 38:488–498

    Article  Google Scholar 

  24. Yang X, Cao J, Ho DWC (2015) Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Cognitive Neurodynam 9(2):113–128

    Article  Google Scholar 

  25. Liu D, Wang D, Zhao D, Wei Q (2012) Neural-network-based optimal control for a class of unknown discrete-time nonlinear systems using globalized dual heuristic programming. IEEE Trans Autom Sci Eng 9:628–634

    Article  Google Scholar 

  26. Yang X, Ho DWC (2015) Synchronization of delayed memristive neural networks: robust analysis approach. IEEE Trans Cybern. doi:10.1109/TCYB.2015.2505903

  27. Liu Q, Dang C, Huang T (2013) A one-layer recurrent neural network for real-time portfolio optimization with probability criterion. IEEE Trans Cybern 43:14–23

    Article  Google Scholar 

  28. Liu Q, Wang J (2013) A one-layer projection neural network for nonsmooth optimzation subject to linear equalities and bound constraints. IEEE Trans Neural Netw Learn Syst 24:812–824

    Article  Google Scholar 

  29. Wen S, Zeng Z, Huang T, Meng Q, Yao W (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26(7):1493–1502

    Article  MathSciNet  Google Scholar 

  30. Wen G, Zhao Y, Duan Z, Yu W, Chen G. Containment of higher-order multi-leader multi-agent systems: a dynamic output approach. IEEE Trans Autom Control 61(4):1135–1140.

  31. Wen S, Zeng Z, Chen M, Huang T (2016) Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2580609

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

    Article  Google Scholar 

  33. Wang L, Zhang R, Xu Z, Peng J (2009) Some characterizations of global exponential stability of a generic class of continuous-time recurrent neural networks. IEEE Trans Syst Man Cybern B Cybern 39:763–772

    Article  Google Scholar 

  34. Zhang C, Zhang H, Wang Z (2011) Novel exponential stability criteria for high-order neural networks with time-varying delays. IEEE Trans Syst Man Cybern B Cybern 41:486–496

    Article  Google Scholar 

  35. Wu L, Feng Z, Lam J (2013) Stability and synchronization of discrete-time neural networks wtih switching parameters and time-varying delays. IEEE Trans Neural Netw Learn Syst 24:1957–1972

    Article  Google Scholar 

  36. Zeng H, He Y, Wu M, Zhang C (2011) Complete delay-decomposing approach to asymptotic stability for neural networks with time-arying delays. IEEE Trans Neural Netw 22:806–812

    Article  Google Scholar 

  37. 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 23:866–875

    Article  Google Scholar 

  38. Li X, Gao H, Yu X (2011) A unified approach to the stability of generalized static neural networks wtih linear fractional uncertainties and delays. IEEE Trans Syst Man Cybern B Cybern 41:1275–1286

    Article  Google Scholar 

  39. Yang X, Huang C, Cao J (2012) An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays. Neural Comput Appl 21(8):2033–2047

    Article  Google Scholar 

  40. Li C, Liao X (2007) Impulsive stabilization of delayed neural networks with and without uncertainty. Int J Robust Nonlinear Control 17(16):1489–1502

    Article  MathSciNet  MATH  Google Scholar 

  41. Wu E, Yang X (2015) Generalized lag synchronization of neural networks with discontinuous activations and bounded perturbations. Circuits Syst Signal Process 34(7):2381–2394

    Article  MathSciNet  MATH  Google Scholar 

  42. Song Q (2009) Design of controller on synchronization of chaotic neural networks with mixed time-varying delays. Neurocomputing 72(13–15):3288–3295

    Article  Google Scholar 

  43. Rakkiyappan R, Chandrasekar A, Park JH, Kwon OM (2014) Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control. Nonlinear Anal Hybrid Syst 14:16–37

    Article  MathSciNet  MATH  Google Scholar 

  44. Chandrasekar A, Rakkiyappan R, Cao JD (2015) Impulsive synchronization of Markovian jumping randomly coupled neural networks with partly unknown transition probabilities via multiple integral approach. Neural Netw 70:27–38

    Article  Google Scholar 

  45. Chandrasekar A, Rakkiyappan R (2016) Impulsive controller design for exponential synchronization of delayed stochastic Memristor-based recurrent neural networks. Neurocomputing 173:1348–1355

    Article  Google Scholar 

  46. Chandrasekar A, Rakkiyappan R, Rihan FA, Lakshmanan S (2014) Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control. Neurocomputing 133:385–398

    Article  Google Scholar 

  47. Rakkiyappan R, Dharani S, Zhu QX (2015) Stochastic sampled-data H-infinity Synchronization of coupled neutral-type delay partial differential systems. J Frankl Inst 352(10):4480–4502

    Article  Google Scholar 

  48. Phat VN, Trinh H (2010) Exponential stabilization of neural networks with various activation functions and mixed time-varying delays. IEEE Trans Neural Netw 21:1180–1184

    Article  Google Scholar 

  49. Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675

    Article  MATH  Google Scholar 

  50. Wang Z, Shu H, Liu Y, Ho DWC, Liu X (2006) Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos Solitons Fractals 30(4):886–896

    Article  MathSciNet  MATH  Google Scholar 

  51. Liu Y, Wang Z, Liu X (2006) On global exponential stability of generalized stochastic neural networks with mixed time delays. Neurocomputing 70(1–3):314–326

    Article  Google Scholar 

  52. Zhao W, Tan Y (2007) Harmless delay for global exponential stability of Cohen–Grossberg neural networks. Math Comput Simul 74:47–57

    Article  MathSciNet  MATH  Google Scholar 

  53. Yue D, Tian E, Zhang Y, Peng C (2009) Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay. IEEE Trans Syst Man Cybern B Cybern 39:503–516

    Article  Google Scholar 

  54. Peng C, Tian Y (2008) Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. J Comput Appl Math 214:480–494

    Article  MathSciNet  MATH  Google Scholar 

  55. Xiong J, Lam J (2009) Stabilization of networked control systems with logic ZOH. IEEE Trans Automat Control 54:358–363

    Article  MathSciNet  MATH  Google Scholar 

  56. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference decision control, Dec 2000, pp 2805–2810

Download references

Author information

Authors and Affiliations

  1. School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yuting Cao & Shiping Wen

  2. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074, China

    Yuting Cao & Shiping Wen

  3. College of Science, Engineering and Technology at Hamad bin Khalifa University, Doha, 23874, Qatar

    Yuting Cao & Shiping Wen

  4. Texas A&M University at Qatar, 23874, Doha, Qatar

    Tingwen Huang

Authors
  1. Yuting Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiping Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tingwen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shiping Wen.

Additional information

This work was supported by the Natural Science Foundation of China under Grants 61673187, 61403152, 61402218, and 61673188.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, Y., Wen, S. & Huang, T. New Criteria on Exponential Lag Synchronization of Switched Neural Networks with Time-Varying Delays. Neural Process Lett 46, 451–466 (2017). https://doi.org/10.1007/s11063-017-9599-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-017-9599-1

Keywords

Search

Navigation