Skip to main content
SpringerLink
Log in

H∞ Filtering for Markovian Switching Genetic Regulatory Networks with Time-Delays and Stochastic Disturbances

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper is concerned with the H ∞ filtering problem for a class of nonlinear Markovian switching genetic regulatory networks (GRNs) with time-delays, intrinsic fluctuation and extrinsic noise. The delays, which exist in both the translation process and feedback regulation process, are not dependent on the system model. The intrinsic fluctuation is described as a state-dependent stochastic process, while the extrinsic noise is modeled as an arbitrary signal with bounded energy, and no exact statistics about the noise are required to be known. The aim of the problem addressed is to design a Markovian jump linear filter to estimate the true concentrations of mRNA and protein through available measurement outputs. By resorting to the Lyapunov functional method and some stochastic analysis tools, it is shown that if a set of linear matrix inequalities (LMIs) is feasible, then the desired linear filter exists. The designed filter ensures asymptotic mean-square stability of the filtering error system and two prescribed L 2-induced gains from the noise signals to the estimation errors. Finally, an illustrative example is given to demonstrate the effectiveness of the approach proposed.

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. L. Chen, K. Alihara, Stability of genetic regulatory networks with time delay. IEEE Trans. Circuits Syst. I 49(5), 602–608 (2002)

    Article  Google Scholar 

  2. F. Chen, J. Cao, Asymptotic and robust stability of genetic regulatory networks with time-varying delays. Neurocomputing 71(4–6), 834–842 (2006)

    Google Scholar 

  3. P. Chen, J. Chen, A Markovian approach to the control of genetic regulatory networks. Biosystems 90(2), 535–545 (2007)

    Article  Google Scholar 

  4. B.S. Chen, Y.C. Wang, On the attenuation and amplification of molecular noise in genetic regulatory networks. BMC Bioinform. 7(52), 1471–2105 (2006)

    Google Scholar 

  5. B.S. Chen, W.S. Wu, Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noise. Math. Biosci. 211(2), 342–355 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Chen, H.L. He, G.M. Church, Modeling gene expression with differential equations. Pac. Symp. Biocomput. 4, 29–40 (1999)

    Google Scholar 

  7. N. Friedman, Graphical inferring cellular networks using probabilistic models. Science 303(5659), 799–805 (2004)

    Article  Google Scholar 

  8. S. Kauffman, Homeostasis and differentiation in random genetic control networks. Nature 224(5215), 177–178 (1969)

    Article  Google Scholar 

  9. S. Kim, H. Li, E.R. Dougherty, N. Cao, Y. Chen, M. Bittner, E.B. Suh, Can Markov chain models mimic biological regulation? J. Biol. Syst. 10(4), 337–357 (2002)

    Article  MATH  Google Scholar 

  10. C. Li, L. Chen, K. Aihara, Stability of genetic networks with sum regulatory logic: Lur’s system and LMI approach. IEEE Trans. Circuits Syst. I 53(11), 2451–2458 (2006)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  12. J. Liang, J. Lam, Z. Wang, State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates. Phys. Lett. A 373(47), 4328–4337 (2009)

    Article  MathSciNet  Google Scholar 

  13. S. Matthew, I. Brian, K. Mads, Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks. Chaos 16(2), 026107:1-15 (2006)

    Google Scholar 

  14. K.M. Nagpal, P.P. Khargonekar, Filtering and smoothing in an H ∞ setting. IEEE Trans. Autom. Control 36(2), 152–166 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  15. C.V. Rao, D.M. Wolf, A.P. Arkin, Control exploitation and tolerance of intracellular noise. Nature 420(6912), 231–237 (2002)

    Article  Google Scholar 

  16. I. Shmulevich, E.R. Dougherty, W. Zhang, Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics 18(10), 1319–1331 (2002)

    Article  Google Scholar 

  17. Y. Sun, F. Gang, J. Cao, Stochastic stability of Markovian switching genetic regulatory networks. Phys. Lett. A 373(18–19), 1646–1652 (2009)

    Article  MathSciNet  Google Scholar 

  18. Y. Wang, Z. Wang, J. Liang, A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Phys. Lett. A 372(39), 6066–6073 (2008)

    Article  Google Scholar 

  19. Z. Wang, J. Lam, G. Wei, K. Fraser, X. Liu, Filtering for nonlinear genetic regulatory networks with stochastic disturbances. IEEE Trans. Autom. Control 53(10), 2448–2457 (2008)

    Article  MathSciNet  Google Scholar 

  20. Z. Wang, X. Liu, Y. Liu, J. Liang, V. Vinciotti, An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series. IEEE Trans. Comput. Biol. Bioinform. 6(3), 411–419 (2009)

    MATH  Google Scholar 

  21. Y. Wang, Z. Ma, J. Shen, Z. Liu, L. Chen, Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations. Math. Biosci. 220(1), 34–44 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. G. Wei, Z. Wang, H. Shu, K. Fraser, X. Liu, Robust filtering for gene expression time series data with variance constraints. Int. J. Comput. Math. 84(5), 619–633 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. G. Wei, Z. Wang, J. Lam, K. Fraser, G.P. Rao, X. Liu, Robust filtering for stochastic genetic regulatory networks with time-varying delay. Math. Biosci. 220(2), 73–80 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  25. S. Xu, T. Chen, J. Lam, Robust H ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Autom. Control 48(5), 900–907 (2003)

    Article  MathSciNet  Google Scholar 

  26. X.L. Zhu, G.H. Yang, New results of stability analysis for systems with time-varying delay. Int. J. Robust Nonlinear Control 20(5), 596–606 (2010)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, People’s Republic of China

    Bo Chen, Li Yu & Wen-An Zhang

  2. Zhejiang Provincial United Key Laboratory of Embedded Systems, Hangzhou, 310023, People’s Republic of China

    Bo Chen, Li Yu & Wen-An Zhang

Authors
  1. Bo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wen-An Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Yu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, B., Yu, L. & Zhang, WA. H∞ Filtering for Markovian Switching Genetic Regulatory Networks with Time-Delays and Stochastic Disturbances. Circuits Syst Signal Process 30, 1231–1252 (2011). https://doi.org/10.1007/s00034-011-9274-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-011-9274-0

Keywords

Search

Navigation