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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 761562, 7 pages
http://dx.doi.org/10.1155/2014/761562
Research Article

State Observer Design for Delayed Genetic Regulatory Networks

1School of Information, Beijing Wuzi University, Beijing 101149, China
2College of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, China
3Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, SK, Canada S7N 5A9
4Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, Canada S7N 5A9

Received 14 March 2014; Accepted 6 May 2014; Published 22 May 2014

Academic Editor: Zhongming Zhao

Copyright © 2014 Li-Ping Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Chen and K. Aihara, “Stability of genetic regulatory networks with time delay,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 5, pp. 602–608, 2002. View at Publisher · View at Google Scholar · View at Scopus
  2. F.-X. Wu, “Delay-independent stability of genetic regulatory networks with time delays,” Advances in Complex Systems, vol. 12, no. 1, pp. 3–19, 2009. View at Google Scholar · View at Scopus
  3. F.-X. Wu, “Stability analysis of genetic regulatory networks with multiple time delays,” in Proceedings of the 29th Annual International Conference of IEEE-EMBS, Engineering in Medicine and Biology Society (EMBC '07), pp. 1387–1390, fra, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Li, L. Chen, and K. Aihara, “Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 11, pp. 2451–2458, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Li, L. Chen, and K. Aihara, “Synchronization of coupled nonidentical genetic oscillators,” Physical Biology, vol. 3, no. 1, pp. 37–44, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. F. Ren and J. Cao, “Asymptotic and robust stability of genetic regulatory networks with time-varying delays,” Neurocomputing, vol. 71, no. 4–6, pp. 834–842, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. F.-X. Wu, “Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties,” IEEE Transactions on Biomedical Circuits and Systems, vol. 5, no. 4, pp. 391–398, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. F.-X. Wu, “Delay-independent stability of genetic regulatory networks,” IEEE Transactions on Neural Networks, vol. 22, no. 11, pp. 1685–1693, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Sinha, Linear Systems: Optimal and Robust Control, CRC Press, New York, NY, USA, 2007.
  10. Z. Wang, D. W. C. Ho, and X. Liu, “State estimation for delayed neural networks,” IEEE Transactions on Neural Networks, vol. 16, no. 1, pp. 279–284, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. He, Q.-G. Wang, M. Wu, and C. Lin, “Delay-dependent state estimation for delayed neural networks,” IEEE Transactions on Neural Networks, vol. 17, no. 4, pp. 1077–1081, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Y. Liu, J. J. Slotine, and A. L. Barabasi, “Observability of complex systems,” Proceedings of the National Academy of Sciences of the USA, vol. 110, no. 7, pp. 2460–2465, 2013. View at Google Scholar
  13. S. Kalir, S. Mangan, and U. Alon, “A coherent feed-forward loop with a SUM input function prolongs flagella expression in Escherichia coli,” Molecular Systems Biology, vol. 1, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Nielsen, J. Villadsen, and G. Liden, Bioreaction Engineering Principles, Kluwer Academic/Plenum Publishers, New York, NY, USA, 2nd edition, 2003.
  15. V. B. Kolmanovskii and A. D. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic, Dodrecht, The Netherlands, 1999.
  16. M. B. Elowitz and S. Leibier, “A synthetic oscillatory network of transcriptional regulators,” Nature, vol. 403, no. 6767, pp. 335–338, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Simon, Optimal State Estimation: Kalman, H and Nonlinear Approaches, Wiley-Interscience, New Jersey, NJ, USA, 2006.
  18. L. P. Tian, Z. K. Shi, L. Z. Liu, and F. X. Wu, “M-Matrix based stability conditions for genetic regulatory networks with time-varying delays and noise perturbations,” IET Systems Biology, vol. 7, no. 5, pp. 214–222, 2013. View at Google Scholar