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Abstract and Applied Analysis
Volume 2014, Article ID 257971, 12 pages
http://dx.doi.org/10.1155/2014/257971
Research Article

Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

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

Received 14 December 2013; Accepted 22 January 2014; Published 2 March 2014

Academic Editor: Xiaojie Su

Copyright © 2014 Yantao Wang 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. F. K. Ahmad, S. Deris, and N. H. Othman, “The inference of breast cancer metastasis through gene regulatory networks,” Journal of Biomedical Informatics, vol. 45, no. 2, pp. 350–362, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. H.-Y. Yeh, S.-W. Cheng, Y.-C. Lin, C.-Y. Yeh, S.-F. Lin, and V.-W. Soo, “Identifying significant genetic regulatory networks in the prostate cancer from microarray data based on transcription factor analysis and conditional independency,” BMC Medical Genomics, vol. 2, article 70, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Somogyi and C. A. Sniegoski, “Modeling the complexity of genetic networks: understanding multigenic and pleiotropic regulation,” Complexity, vol. 1, no. 6, pp. 45–63, 1995/96. View at Publisher · View at Google Scholar · View at MathSciNet
  4. D. C. Weaver, C. T. Workman, and G. D. Stormo, “Modeling regulatory networks with weight matrices,” in Proceedings of the Pacific Symposium on Biocomputing, vol. 4, pp. 112–123, World Scientific, Maui, Hawaii, 1999.
  5. 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
  6. T. Chen, H. L. He, and G. M. Church, “Modeling gene expression with differential equations,” Pacific Symposium on Biocomputing, vol. 4, pp. 29–40, 1999. View at Google Scholar · View at Scopus
  7. D. Thieffry and R. Thomas, “Qualitative analysis of gene networks,” Pacific Symposium on Biocomputing, vol. 3, pp. 77–88, 1998. View at Google Scholar · View at Scopus
  8. L. Chen and K. Aihara, “Stability of genetic regulatory networks with time delay,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 5, pp. 602–608, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. Zhang, A. H. Yu, and G. D. Zhang, “M-matrix-based delay-range-dependent global asymptotical stability criterion for genetic regulatory networks with time-varying delays,” Neurocomputing, vol. 113, pp. 8–15, 2013. View at Publisher · View at Google Scholar
  10. Y. He, J. Zeng, M. Wu, and C.-K. Zhang, “Robust stabilization and H controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties,” Mathematical Biosciences, vol. 236, no. 1, pp. 53–63, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. F.-X. Wu, “Stability and bifurcation of ring-structured genetic regulatory networks with time delays,” IEEE Transactions on Circuits and Systems I, vol. 59, no. 6, pp. 1312–1320, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Y. T. Wang, A. H. Yu, and X. Zhang, “Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach,” Neural Computing and Applications, vol. 23, no. 5, pp. 1217–1227, 2013. View at Publisher · View at Google Scholar
  13. J. H. Koo, D. H. Ji, S. C. Won, and J. H. Park, “An improved robust delay-dependent stability criterion for genetic regulatory networks with interval time delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 8, pp. 3399–3405, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Liu and D. Yue, “Asymptotic and robust stability of T-S fuzzy genetic regulatory networks with time-varying delays,” International Journal of Robust and Nonlinear Control, vol. 22, no. 8, pp. 827–840, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. W. Wang and S. Zhong, “Delay-dependent stability criteria for genetic regulatory networks with time-varying delays and nonlinear disturbance,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 9, pp. 3597–3611, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. P. Li, J. Lam, and Z. Shu, “On the transient and steady-state estimates of interval genetic regulatory networks,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 40, no. 2, pp. 336–349, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. B. Lv, J. Liang, and J. Cao, “Robust distributed state estimation for genetic regulatory networks with Markovian jumping parameters,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4060–4078, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J. Liang, J. Lam, and Z. Wang, “State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates,” Physics Letters A, vol. 373, no. 47, pp. 4328–4337, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. W. Yu, J. Lü, G. Chen, Z. Duan, and Q. Zhou, “Estimating uncertain delayed genetic regulatory networks: an adaptive filtering approach,” IEEE Transactions on Automatic Control, vol. 54, no. 4, pp. 892–897, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  20. M. Mohammadian, A. Hossein Abolmasoumi, and H. Reza Momeni, “H mode-independent filter design for Markovian jump genetic regulatory networks with time-varying delays,” Neurocomputing, vol. 87, pp. 10–18, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. B. Chen, L. Yu, and W.-A. Zhang, “H filtering for Markovian switching genetic regulatory networks with time-delays and stochastic disturbances,” Circuits, Systems, and Signal Processing, vol. 30, no. 6, pp. 1231–1252, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. W. Wang, S. Zhong, and F. Liu, “Robust filtering of uncertain stochastic genetic regulatory networks with time-varying delays,” Chaos, Solitons & Fractals, vol. 45, no. 7, pp. 915–929, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. D. Zhang, L. Yu, and Q.-G. Wang, “Exponential H filtering for switched stochastic genetic regulatory networks with random sensor delays,” Asian Journal of Control, vol. 13, no. 5, pp. 749–755, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. T. Wang, Y. S. Ding, L. Zhang, and K. R. Hao, “Robust state estimation for discrete-time stochastic genetic regulatory networks with probabilistic measurement delays,” Neurocomputing, vol. 111, pp. 1–12, 2013. View at Publisher · View at Google Scholar
  25. D. Zhang, H. Song, L. Yu, Q.-G. Wang, and C. Ong, “Set-values filtering for discrete time-delay genetic regulatory networks with time-varying parameters,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 693–703, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. A. Liu, L. Yu, W.-A. Zhang, and B. Chen, “H filtering for discrete-time genetic regulatory networks with random delays,” Mathematical Biosciences, vol. 239, no. 1, pp. 97–105, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J. Cao and F. Ren, “Exponential stability of discrete-time genetic regulatory networks with delays,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 520–523, 2008. View at Publisher · View at Google Scholar · View at Scopus
  28. Q. Ye and B. Cui, “Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties,” Cognitive Neurodynamics, vol. 4, no. 2, pp. 165–176, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. Q. Ma, S. Xu, Y. Zou, and J. Lu, “Robust stability for discrete-time stochastic genetic regulatory networks,” Nonlinear Analysis. Real World Applications, vol. 12, no. 5, pp. 2586–2595, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. K. Mathiyalagan and R. Sakthivel, “Robust stabilization and H control for discrete-time stochastic genetic regulatory networks with time delays,” Canadian Journal of Physics, vol. 90, no. 10, pp. 939–953, 2012. View at Publisher · View at Google Scholar
  31. K. Mathiyalagan, R. Sakthivel, and S. M. Anthoni, “New robust passivity criteria for discrete-time genetic regulatory networks with Markovian jumping parameters,” Canadian Journal of Physics, vol. 90, no. 2, pp. 107–118, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. L. G. Wu, X. J. Su, and P. Shi, “Output feedback control of Markovian jump repeated scalar nonlinear systems,” IEEE Transactions on Automatic Control, vol. 59, no. 1, pp. 199–204, 2014. View at Publisher · View at Google Scholar
  33. L. Wu, P. Shi, and H. Gao, “State estimation and sliding-mode control of Markovian jump singular systems,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1213–1219, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  34. L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems,” Automatica, vol. 48, no. 8, pp. 1929–1933, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. L. Wu, P. Shi, H. Gao, and C. Wang, “H filtering for 2D Markovian jump systems,” Automatica, vol. 44, no. 7, pp. 1849–1858, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. L. Wu, X. Yao, and W. X. Zheng, “Generalized H2 fault detection for two-dimensional Markovian jump systems,” Automatica, vol. 48, no. 8, pp. 1741–1750, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  37. X. J. Su, L. G. Wu, and P. Shi, “Sensor networks with random link failures: distributed filtering for T-S fuzzy systems,” IEEE Transactions on Industrial Informatics, vol. 9, no. 3, pp. 1739–1750, 2013. View at Publisher · View at Google Scholar
  38. L. Wu and D. W. C. Ho, “Fuzzy filter design for Itô stochastic systems with application to sensor fault detection,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 1, pp. 233–242, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. X. Su, P. Shi, L. Wu, and S. K. Nguang, “Induced filtering of fuzzy stochastic systems with time-varying delays,” IEEE Transactions on Computers, vol. 43, no. 4, pp. 1251–1264, 2012. View at Google Scholar
  40. A. Hmamed, C. E. Kasri, E. H. Tissir, T. Alvarez, and F. Tadeo, “Robust H filtering for uncertain 2-D continuous systems with delays,” International Journal of Innovative Computing Information and Control, vol. 9, no. 5, pp. 2167–2183, 2013. View at Google Scholar
  41. F. B. Li and X. Zhang, “Delay-range-dependent robust H1 filtering for singular LPV systems with time variant delay,” International Journal of Innovative Computing Information and Control, vol. 9, no. 1, pp. 339–353, 2013. View at Google Scholar
  42. J. Liang and J. Lam, “Robust state estimation for stochastic genetic regulatory networks,” International Journal of Systems Science, vol. 41, no. 1, pp. 47–63, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  43. M. C. de Oliveira, J. Bernussou, and J. C. Geromel, “A new discrete-time robust stability condition,” Systems & Control Letters, vol. 37, no. 4, pp. 261–265, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet