Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 659251, 10 pages
http://dx.doi.org/10.1155/2013/659251
Research Article

Exponential Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations

1Sichuan Provincial key Lab of Power System Wide-Area Measurement and Control, University of Electronic Science and Technology of China, Chengdu 611731, China
2School of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China

Received 12 August 2013; Revised 21 November 2013; Accepted 28 November 2013

Academic Editor: Weihai Zhang

Copyright © 2013 Zhaohui Chen and Qi 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. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhäauser, Boston, Mass, USA, 2003.
  2. E. Fridman and U. Shaked, “A descriptor system approach to H control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  3. F. Gouaisbaut and D. Peaucelle, “A note on stability of time delay systems,” in Proceedings of the IFAC Symposium on Robust Control Design, Toulouse, France, 2006. View at Scopus
  4. X. M. Zhang and Q. L. Han, “A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays,” International Journal of Robust and Nonlinear Control, vol. 19, no. 17, pp. 1922–1930, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. T. L. Hsien and C. H. Lee, “Robust stability of discrete bilinear uncertain time-delay systems,” Circuits, Systems, and Signal Processing, vol. 30, no. 6, pp. 1417–1443, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. Shi, R. K. Agarwal, E. K. Boukas, and Y. Shi, “Optimal guaranteed cost control of uncertain discrete time-delay systems,” Journal of Computational and Applied Mathematics, vol. 157, no. 2, pp. 435–451, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Ma and E. K. Boukas, “Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay,” IET Control Theory & Applications, vol. 3, no. 9, pp. 1217–1225, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Wu and D. W. C. Ho, “Reduced-order L2L filtering for a class of nonlinear switched stochastic systems,” IET Control Theory & Applications, vol. 3, no. 5, pp. 493–508, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. H. Gao and C. Wang, “Robust L2L filtering for uncertain systems with multiple time-varying state delays,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 4, pp. 594–599, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. C. Lin, Q. G. Wang, and T. H. Lee, “A less conservative robust stability test for linear uncertain time-delay systems,” IEEE Transactions on Automatic Control, vol. 51, no. 1, pp. 87–91, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  11. H. Zhang and Z. Liu, “Stability analysis for linear delayed systems via an optimally dividing delay interval approach,” Automatica, vol. 47, no. 9, pp. 2126–2129, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Q. L. Han, “A discrete delay decomposition approach to stability of linear retarded and neutral systems,” Automatica, vol. 45, no. 2, pp. 517–524, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. B. Zhang and Y. Li, “Exponential L2L filtering for distributed delay systems with Markovian jumping parameters,” Signal Processing, vol. 93, no. 1, pp. 206–216, 2013. View at Publisher · View at Google Scholar
  14. Z. Feng and J. Lam, “Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 22, no. 6, pp. 676–689, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. Liu, Z. Wang, and X. Liu, “Robust H control for a class of nonlinear stochastic systems with mixed time delay,” International Journal of Robust and Nonlinear Control, vol. 17, no. 16, pp. 1525–1551, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Wu and W. Zhou, “Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays,” Journal of Control Theory and Applications, vol. 6, no. 2, pp. 171–176, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  17. J. Wu, G. Lu, S. Wo, and X. Xiao, “Exponential stability and stabilization for nonlinear descriptor systems with discrete and distributed delays,” International Journal of Robust and Nonlinear Control, vol. 23, no. 12, pp. 1393–1404, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. S. Mahmoud, A. Y. Al-Rayyah, and Y. Xia, “Quantised feedback stabilization of interconnected discrete-delay systems,” IET Control Theory & Applications, vol. 5, no. 6, pp. 795–802, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L. Wu, X. Su, P. Shi, and J. Qiu, “A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 1, pp. 273–286, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. E. Wang, X. M. Sun, and J. Zhao, “Stabilization of a class of switched stochastic systems with time delays under asynchronous switching,” Circuits, Systems, and Signal Processing, vol. 32, no. 1, pp. 347–360, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  21. S. Xie and L. Xie, “Stabilization of a class of uncertain large-scale stochastic systems with time delays,” Automatica, vol. 36, no. 1, pp. 161–167, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. D. Yue and S. Won, “Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties,” Electronics Letters, vol. 37, no. 15, pp. 992–993, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. D. Yue and Q. L. Han, “Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching,” IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 217–222, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  24. S. Xu, J. Lam, X. Mao, and Y. Zou, “A new LMI condition for delay-dependent robust stability of stochastic time-delay systems,” Asian Journal of Control, vol. 7, no. 4, pp. 419–423, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  25. R. Yang, P. Shi, and H. Gao, “New delay-dependent stability criterion for stochastic systems with time delays,” IET Control Theory & Applications, vol. 2, no. 11, pp. 966–973, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  26. P. Cheng, F. Deng, and Y. Peng, “Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay,” Journal of Systems Engineering and Electronics, vol. 22, no. 5, pp. 799–809, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Xu and T. Chen, “Robust H control for uncertain stochastic systems with state delay,” IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 2089–2094, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  28. S. Xu and T. Chen, “H output feedback control for uncertain stochastic systems with time-varying delays,” Automatica, vol. 40, no. 12, pp. 2091–2098, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. E. K. Boukas and Z. K. Liu, “Robust H filtering for polytopic uncertain time-delay systems with Markov jumps,” Computers and Electrical Engineering, vol. 28, no. 3, pp. 171–193, 2002. View at Publisher · View at Google Scholar · View at Scopus
  30. W. Zhang, B. S. Chen, and C. S. Tseng, “Robust H filtering for nonlinear stochastic systems,” IEEE Transactions on Signal Processing, vol. 53, no. 2, pp. 589–598, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  31. W. Zhang, B. S. Chen, L. Sheng, and M. Gao, “Robust H2/H filter design for a class of nonlinear stochastic systems with state-dependent noise,” Mathematical Problems in Engineering, vol. 2012, Article ID 750841, 16 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. 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 Zentralblatt MATH · View at MathSciNet
  33. Z. Wang, F. Yang, D. W. C. Ho, and X. Liu, “Robust H filtering for stochastic time-delay systems with missing measurements,” IEEE Transactions on Signal Processing, vol. 54, no. 7, pp. 2579–2587, 2006. View at Publisher · View at Google Scholar · View at Scopus
  34. J. Xia, S. Xu, and B. Song, “Delay-dependent L2L 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
  35. Y. Chen, A. Xue, and S. Zhou, “New delay-dependent L2L filter design for stochastic time-delay systems,” Signal Processing, vol. 89, no. 6, pp. 974–980, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. R. Yang, H. Gao, and P. Shi, “Delay-dependent L2L filter design for stochastic time-delay systems,” IET Control Theory & Applications, vol. 5, no. 1, pp. 1–8, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  37. R. Yang, H. Gao, P. Shi, and L. Zhang, “Delay-dependent energy-to-peak filter design for stochastic systems with time delay: a delay partitioning approach,” in Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC/CCC '09), pp. 5472–5477, Shanghai, China, December 2009. View at Publisher · View at Google Scholar · View at Scopus
  38. L. Li and Y. Jia, “Robust L2L filtering for stochastic systems with discrete and distributed time-varying delays,” Asian Journal of Control, vol. 14, no. 4, pp. 1047–1058, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  39. Z. Wang, Y. Liu, and X. Liu, “Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays,” IEEE Transactions on Automatic Control, vol. 55, no. 7, pp. 1656–1662, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  40. K. Gu, “An integral inequality in the stability problem of time-delay systems,” in Proceedings of the 39th IEEE Confernce on Decision and Control, pp. 2805–2810, Sydney, Australia, December 2000. View at Scopus