Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 808973, 16 pages
http://dx.doi.org/10.1155/2015/808973
Research Article

Robust Filtering for Uncertain Neutral Stochastic Systems with Markovian Jumping Parameters and Time Delay

Institute of Electronic and Information Engineering, Shunde Polytechnic, Foshan 528300, China

Received 15 March 2015; Revised 4 April 2015; Accepted 12 May 2015

Academic Editor: Son Nguyen

Copyright © 2015 Yajun Li and Zhaowen Huang. 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. X.-G. Liu, M. Wu, R. Martin, and M.-L. Tang, “Delay-dependent stability analysis for uncertain neutral systems with time-varying delays,” Mathematics and Computers in Simulation, vol. 75, no. 1-2, pp. 15–27, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. O. M. Kwon, J. H. Park, and S. M. Lee, “On robust stability criterion for dynamic systems with time-varying delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 937–942, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. W.-H. Chen, Z.-H. Guan, and X. Lu, “Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach,” Systems & Control Letters, vol. 54, no. 6, pp. 547–555, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. O. M. Kwon, J. H. Park, and S. M. Lee, “On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 864–873, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Q. Zhu and J. Cao, “Robust exponential stability of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 21, no. 8, pp. 1314–1325, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. Q. Zhu and J. Cao, “Mean-square exponential input-to-state stability of stochastic delayed neural networks,” Neurocomputing, vol. 131, no. 6, pp. 157–163, 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. Chen, A. Xue, S. Zhou, and R. Lu, “Delay-dependent robust control for uncertain stochastic time-delay systems,” Circuits, Systems, and Signal Processing, vol. 27, no. 4, pp. 447–460, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. Q. Zhu, J. Cao, and R. Rakkiyappan, “Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays,” Nonlinear DynamicsSystems, vol. 79, no. 2, pp. 1085–1098, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  9. M. Hua, H. Tan, J. Chen, and J. Fei, “Robust delay-range-dependent non-fragile H filtering for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays,” Journal of the Franklin Institute, vol. 352, no. 3, pp. 1318–1341, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Q. Zhu and J. Cao, “Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 41, no. 2, pp. 341–353, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Hua, F. Deng, X. Liu, and Y. Peng, “Robust delay-dependent exponential stability of uncertain stochastic system with time-varying delay,” Circuits, Systems, and Signal Processing, vol. 29, no. 3, pp. 515–526, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. Q. Zhu and B. Song, “Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays,” Nonlinear Analysis: Real World Applications, vol. 12, no. 5, pp. 2851–2860, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. G. Chen and Y. Shen, “Robust H filter design for neutral stochastic uncertain systems with time-varying delay,” Journal of Mathematical Analysis and Applications, vol. 353, no. 1, pp. 196–204, 2009. View at Publisher · View at Google Scholar
  14. H. Li and M. Fu, “A linear matrix inequality approach to robust H filtering,” IEEE Transactions on Signal Processing, vol. 45, no. 9, pp. 2338–2350, 1997. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Liu, F. Sun, K. He, and Z. Sun, “Design of reduced-order H filter for Markovian jumping systems with time delay,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 51, no. 11, pp. 607–612, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Lian, Z. Feng, and P. Shi, “Robust H filtering for a class of uncertain stochastic hybrid neutral systems with timevarying delay,” International Journal of Adaptive Control and Signal Processing, vol. 27, no. 6, pp. 462–477, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. L. Ma and F. Da, “Exponential H filter design for stochastic time-varying delay systems with Markovian jumping parameters,” International Journal of Robust and Nonlinear Control, vol. 20, no. 7, pp. 802–817, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. B. Song, S. Xu, and Y. Zou, “Delay-dependent robust H filtering for uncertain neutral stochastic time-delay systems,” Circuits, Systems, and Signal Processing, vol. 28, no. 2, pp. 241–256, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. B. Song, S. Xu, J. Xia, Y. Zou, and Q. Chen, “Design of robust H filters for a class of uncertain nonlinear neutral stochastic systems with time delays,” International Journal of Systems Science. Principles and Applications of Systems and Integration, vol. 42, no. 4, pp. 633–642, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. Y. Chen and W. X. Zheng, “Exponential H filtering for stochastic Markovian jump systems with time delays,” International Journal of Robust and Nonlinear Control, vol. 24, no. 4, pp. 625–643, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. S. Xu, J. Lam, H. Gao, and Y. Zou, “Robust H filtering for uncertain discrete stochastic systems with time delays,” Circuits, Systems, and Signal Processing, vol. 24, no. 6, pp. 753–770, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. S. Xu and T. Chen, “Robust H filtering for uncertain stochastic time-delay systems,” Asian Journal of Control, vol. 5, no. 3, pp. 364–373, 2003. View at Google Scholar · View at Scopus
  23. H. Gao, J. Lam, and C. Wang, “Robust energy-to-peak filter design for stochastic time-delay systems,” Systems & Control Letters, vol. 55, no. 2, pp. 101–111, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. L. Li, Y. Jia, J. Du, and H. Kokame, “L2-L filter design for neutral stochastic time-delay systems,” in Proceedings of the 49th IEEE Conference Decision and Control, pp. 2644–2649, Atlanta, Ga, USA, 2010.
  25. J. Xia, S. Xu, and B. Song, “Delay-dependent L2-L filter design for stochastic time-delay systems,” Systems & Control Letters, vol. 56, no. 9-10, pp. 579–587, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. N. Krasovskii and E. Lidskii, “Analytical design of controllers in systems with random attributes I,” Automation and Remote Control, vol. 22, no. 1, pp. 1021–1025, 1961. View at Google Scholar
  27. Q. Zhu and J. Cao, “Stability analysis of markovian jump stochastic BAM neural networks with impulse control and mixed time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 3, pp. 467–479, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Zhang and E.-K. Boukas, “Mode-dependent H filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities,” Automatica, vol. 45, no. 6, pp. 1462–1467, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. Q. Zhu and J. Cao, “Stability of Markovian jump neural networks with impulse control and time varying delays,” Nonlinear Analysis. Real World Applications, vol. 13, no. 5, pp. 2259–2270, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. L. Zhang and E.-K. Boukas, “H control for discrete-time Markovian jump linear systems with partly unknown transition probabilities,” International Journal of Robust and Nonlinear Control, vol. 19, no. 8, pp. 868–883, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. Q. Zhu, “pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching,” Journal of the Franklin Institute, vol. 351, no. 7, pp. 3965–3986, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. X. Yao, L. Wu, W. X. Zheng, and C. Wang, “Robust H filtering of Markovian jump stochastic systems with uncertain transition probabilities,” International Journal of Systems Science, vol. 42, no. 7, pp. 1219–1230, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. Y. Chen and W. X. Zheng, “L2-L filtering for stochastic Markovian jump delay systems with nonlinear perturbations,” Signal Processing, vol. 109, no. 3, pp. 154–164, 2015. View at Publisher · View at Google Scholar
  34. Y. Chen, W. X. Zheng, and A. Xue, “A new result on stability analysis for stochastic neutral systems,” Automatica, vol. 46, no. 12, pp. 2100–2104, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus