Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2017, Article ID 4573039, 17 pages
https://doi.org/10.1155/2017/4573039
Research Article

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

1College of Automation, Harbin Engineering University, Harbin 150001, China
2Graduate Department, Harbin University of Science and Technology, Harbin 150080, China
3College of Science, Harbin Engineering University, Harbin 150001, China
4College of Science, Harbin University of Science and Technology, Harbin 150080, China

Correspondence should be addressed to Yanfeng Zhao; nc.ude.tsubrh@gnefnayoahz

Received 10 March 2017; Accepted 21 May 2017; Published 2 October 2017

Academic Editor: Dimitri Volchenkov

Copyright © 2017 Yanfeng Zhao 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 MathSciNet · View at Scopus
  2. G. Chesi and Y. S. Hung, “Stability analysis of uncertain genetic sum regulatory networks,” Automatica. A Journal of IFAC, the International Federation of Automatic Control, vol. 44, no. 9, pp. 2298–2305, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. 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
  4. M. Chaves, E. D. Sontag, and R. Albert, “Methods of robustness analysis for Boolean models of gene control networks,” IEE Proceedings: Systems Biology, vol. 153, no. 4, pp. 154–167, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Han, Y. Liu, and Y. Tu, “Controllability of Boolean control networks with time delays both in states and inputs,” Neurocomputing, vol. 129, pp. 467–475, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. H. de Jong, “Modeling and simulation of genetic regulatory systems: a literature review,” Journal of Computational Biology, vol. 9, no. 1, pp. 67–103, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. I. Ivanov and E. R. Dougherty, “Modelling genetic regulatory networks: continuous or discrete,” Journal of Biological Systems, vol. 2, no. 2, pp. 219–229, 2011. View at Google Scholar
  8. Y. Liu, F. E. Alsaadi, X. Yin, and Y. Wang, “Robust H∞ filtering for discrete nonlinear delayed stochastic systems with missing measurements and randomly occurring nonlinearities,” International Journal of General Systems, vol. 44, no. 2, pp. 169–181, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. Zhang, L. Wu, and S. Cui, “An improved integral inequality to stability analysis of genetic regulatory networks with interval time-varying delays,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 12, no. 2, pp. 398–409, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Zhang, J.-A. Fang, and Y. Tang, “New robust stability analysis for genetic regulatory networks with random discrete delays and distributed delays,” Neurocomputing, vol. 74, no. 14-15, pp. 2344–2360, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Rakkiyappan, S. Lakshmanan, and P. Balasubramaniam, “Delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with time-varying delays,” Circuits, Systems, and Signal Processing, vol. 32, no. 3, pp. 1147–1177, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. Hu, Z. Wang, B. Shen, and H. Gao, “Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays,” IEEE Transactions on Signal Processing, vol. 61, no. 5, pp. 1230–1238, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Y. Wang, J. Cao, and L. Li, “Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations,” Cognitive Neurodynamics, vol. 4, no. 1, pp. 81–90, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. 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
  15. Q. Li, B. Shen, Y. Liu, and F. E. Alsaadi, “Event-triggered H state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays,” Neurocomputing, vol. 174, pp. 912–920, 2016. View at Publisher · View at Google Scholar
  16. 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 · View at Scopus
  17. 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
  18. X. Wan, L. Xu, H. Fang, and F. Yang, “Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays,” Neurocomputing, vol. 124, no. 2, pp. 72–80, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Zhao, J. Shen, and D. Chen, “New stability criterion for discrete-time genetic regulatory networks with time-varying delays and stochastic disturbances,” Mathematical Problems in Engineering, Article ID 7634680, Art. ID 7634680, 13 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. J. Hu, Z. Wang, D. Chen, and F. E. Alsaadi, “Estimation, filtering and fusion for networked systems with network-induced phenomena: new progress and prospects,” Information Fusion, vol. 31, pp. 65–75, 2016. View at Publisher · View at Google Scholar
  21. S. Lakshmanan, J. H. Park, H. Y. Jung, P. Balasubramaniam, and S. M. Lee, “Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties,” BioSystems, vol. 111, no. 1, pp. 51–70, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Balasubramaniam and L. J. Banu, “Robust state estimation for discrete-time genetic regulatory network with random delays,” Neurocomputing, vol. 122, pp. 349–369, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Hu, Z. Wang, B. Shen, and H. Gao, “Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements,” International Journal of Control, vol. 86, no. 4, pp. 650–663, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Probability-guaranteed H∞ finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations,” Systems & Control Letters, vol. 61, no. 4, pp. 477–484, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  25. R. Anbuvithya, K. Mathiyalagan, R. Sakthivel, and P. Prakash, “Sampled-data state estimation for genetic regulatory networks with time-varying delays,” Neurocomputing, vol. 151, no. 2, pp. 737–744, 2015. View at Publisher · View at Google Scholar · View at Scopus
  26. J. Hu, Z. Wang, S. Liu, and H. Gao, “A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements,” Automatica. A Journal of IFAC, the International Federation of Automatic Control, vol. 64, pp. 155–162, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. R. Sakthivel, K. Mathiyalagan, S. Lakshmanan, and J. H. Park, “Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties,” Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, vol. 74, no. 4, pp. 1297–1315, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. J. Hu, D. Chen, and J. Du, “State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays,” International Journal of General Systems, vol. 43, no. 3-4, pp. 387–401, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. H. Dong, Z. Wang, S. X. Ding, and H. Gao, “Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization,” Automatica. A Journal of IFAC, the International Federation of Automatic Control, vol. 52, pp. 355–362, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 3008–3015, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. T. H. Lee, J. H. Park, Z.-G. Wu, S.-C. Lee, and D. H. Lee, “Robust rH∞ decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties,” Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, vol. 70, no. 1, pp. 559–570, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  32. J. Hu, S. Liu, D. Ji, and S. Li, “On co-design of filter and fault estimator against randomly occurring nonlinearities and randomly occurring deception attacks,” International Journal of General Systems, vol. 45, no. 5, pp. 619–632, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. L. H. Keel and S. P. Bhattacharyya, “Robust, fragile, or optimal?” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 42, no. 8, pp. 1098–1105, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. Y. Yajing, D. Hongli, Z. Wangb, W. Rena, and F. E. Alsaadic, “Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties,” Neurocomputing, vol. 182, pp. 18–24, 2016. View at Publisher · View at Google Scholar
  35. J. Hu, J. Liang, D. Chen, D. Ji, and J. Du, “A recursive approach to non-fragile filtering for networked systems with stochastic uncertainties and incomplete measurements,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 352, no. 5, pp. 1946–1962, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. N. Hou, H. Dong, Z. Wang, W. Ren, and F. E. Alsaadi, “Non-fragile state estimation for discrete Markovian jumping neural networks,” Neurocomputing, vol. 179, pp. 238–245, 2016. View at Publisher · View at Google Scholar
  37. P. T. Nam, P. N. Pathirana, and H. Trinh, “Discrete Wirtinger-based inequality and its application,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 352, no. 5, pp. 1893–1905, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, vol. 15 of SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  39. P. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica. A Journal of IFAC, the International Federation of Automatic Control, vol. 47, no. 1, pp. 235–238, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. L. Lu, B. He, C. Man, and S. Wang, “Robust state estimation for Markov jump genetic regulatory networks based on passivity theory,” Complexity, vol. 21, no. 5, pp. 214–223, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. Y. Liu, W. Liu, M. A. Obaid, and I. A. Abbas, “Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays,” Neurocomputing, vol. 177, pp. 409–415, 2016. View at Publisher · View at Google Scholar · View at Scopus
  42. J. Zhang, L. Ma, and Y. Liu, “Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects,” Neurocomputing, vol. 216, pp. 657–665, 2016. View at Publisher · View at Google Scholar · View at Scopus
  43. J. Hu, Z. Wang, F. E. Alsaadi, and T. Hayat, “Event-based filtering for time-varying nonlinear systems subject to multiple missing measurements with uncertain missing probabilities,” Information Fusion, vol. 38, pp. 74–83, 2017. View at Publisher · View at Google Scholar
  44. S. Liu, G. Wei, Y. Song, and Y. Liu, “Extended Kalman filtering for stochastic nonlinear systems with randomly occurring cyber attacks,” Neurocomputing, 2016. View at Publisher · View at Google Scholar · View at Scopus