Skip to main content
SpringerLink
Log in

Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach

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

Abstract

This paper is concerned with the problem of the globally asymptotically mean square stability for a class of delayed genetic regularity networks (GRNs) with both parameter uncertainties and stochastic disturbances, where the time delays are belong to given intervals and assumed to be time varying. Based on choosing an appropriate and novel Lyapunov functional, a “delay fractioning” approach that is different from the existing ones is introduced. By utilizing \(It\hat{o}\hbox{'}s\) differential formula and using the linear matrix inequality (LMI) method, we derive a robust asymptotical stability criterion in mean square sense for uncertain GRNs with time-varying delays. All the stability conditions are given in terms of LMIs. One example and its simulation are provided to show the advantages of the obtained result.

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. Gao H, Li X (2011) \(H^{\infty}\) filtering for discrete-time state-delayed systems with finite frequency specifications. IEEE Trans Automat Control 56(12):2935–2941

    Article  Google Scholar 

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

  3. Li C, Chen L, Aihara K (2007) Stochastic stability of genetic networks with disturbance attenuation. IEEE Trans Circuits Syst 54(10):892–896

    Article  Google Scholar 

  4. Li H, Gao H, Shi P (2010) New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans Neural Netw 21(11):1842–1847

    Article  Google Scholar 

  5. Li H, Liu H, Gao H, Shi P (2011) Reliable fuzzy control for active suspension systems with actuator delay and fault. IEEE Trans Fuzzy Syst 20(2):342–357

    Article  Google Scholar 

  6. Li P, Lam J, Shu Z (2010) On the transient and steady-state estimates of interval genetic regulatory networks. IEEE Trans Syst Man Cybern B Cybern 40(2):336–349

    Article  Google Scholar 

  7. Li X, Gao H, Yu X (2011) A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays. IEEE Trans Syst Man Cybern B Cybern 41(5):1275–1286

    Article  MathSciNet  Google Scholar 

  8. Sun Y, Feng G (2008) Stability of stochastic genetic regulatory networks. In: Proceedings of 2nd international symposium on optimization system biology, pp 123–129

  9. Wang G, Cao J (2009) Robust exponential stability analysis for stochastic genetic networks with uncertain parameters. Commun Nonlinear Sci Numer Simulat 14(8):3369–3378

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang Y, Cao J, Li L (2010) Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations. Cogn Neurodyn 4(1):81–90

    Article  MathSciNet  Google Scholar 

  11. Wang Y, Wang Z, Liang J (2010) On robust stability of stochastic genetic regulatory networks with time delays: a delay fractioning approach. IEEE Trans Syst Man Cybern B Cybern 40(3):729–740

    Article  Google Scholar 

  12. Wang Y, Xie L, de Souza CE (1992) Robust control of a class of uncertain nonlinear systems. Syst Control Lett 19(2):139–149

    Article  Google Scholar 

  13. Wang Z, Liao X, Guo S, Wu H (2011) Mean square exponential stability of stochastic genetic regulatory networks with time-varying delays. Inform Sci 181(4):792–811

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang Z, Liu G, Sun Y, Wu H (2009) Robust stability of stochastic delayed genetic regulatory networks. Cogn Neurodyn 3(3):271–280

    Article  Google Scholar 

  15. Wu H, Liao X, Guo S, Feng W, Wang Z (2009) Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays. Neurocomputing 72(13–15):3263–3276

    Article  Google Scholar 

  16. Zhou Q, Xu S, Chen B, Li H, Chu Y (2009) Stability analysis of delayed genetic regulatory networks with stochastic disturbances. Phys Lett A 373(41):3715–3723

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work is partially supported by the fund Heilongjiang Education Committee under Grant No. 12521429, the fund of Heilongjiang University Innovation Team Support Plan under Grant No. Hdtd2010–03 and the fund of Heilongjiang University Student Academic and Technological Innovation Projects. The authors thank the anonymous referees for their helpful comments and suggestions that improve greatly this note.

Author information

Authors and Affiliations

  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Yantao Wang, Ahui Yu & Xian Zhang

Authors
  1. Yantao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahui Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xian Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Y., Yu, A. & Zhang, X. Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach. Neural Comput & Applic 23, 1217–1227 (2013). https://doi.org/10.1007/s00521-012-1034-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-1034-y

Keywords

Search

Navigation