Table of Contents
International Journal of Stochastic Analysis
Volume 2013, Article ID 306707, 9 pages
http://dx.doi.org/10.1155/2013/306707
Research Article

Filtering for Discrete-Time Stochastic Systems with Nonlinear Sensor and Time-Varying Delay

1College of Computer and Information, Hohai University, Changzhou 213022, China
2Changzhou Key Laboratory of Sensor Networks and Environmental Sensing, Changzhou 213022, China
3Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Changzhou 213022, China
4School of Mathematical Sciences, Anhui University, Hefei 230601, China
5Department of Mathematics and Physics, Hohai University, Changzhou 213022, China

Received 30 November 2012; Revised 17 February 2013; Accepted 17 February 2013

Academic Editor: H. Srivastava

Copyright © 2013 Mingang Hua 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. M. Malek-Zavarei and M. Jamshidi, Time-Delay Systems: Analysis, Optimization and Application, North-Holland, Amsterdam, The Netherlands, 1987.
  2. L. Dugard and E. I. Verriet, Stability and Control of Time-Delay Systems, Springer, Berlin, Germany, 1997.
  3. V. B. Kolmanovskii and A. D. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer, Dordrecht, The Netherlands, 1999.
  4. S. P. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.
  5. K. Gu, V. L. Kharitonov, and J. Chen, Stability of time-delay systems, Birkhäauser, Boston, Mass, USA, 2003.
  6. B. Zhang, S. Xu, and Y. Zou, “Improved stability criterion and its applications in delayed controller design for discrete-time systems,” Automatica, vol. 44, no. 11, pp. 2963–2967, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. X. Meng, J. Lam, B. Du, and H. Gao, “A delay-partitioning approach to the stability analysis of discrete-time systems,” Automatica, vol. 46, no. 3, pp. 610–614, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Shao and Q. L. Han, “New stability criteria for linear discrete-time systems with interval-like time-varying delays,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 619–625, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Liu and J. Zhang, “Note on stability of discrete-time time-varying delay systems,” IET Control Theory & Applications, vol. 6, no. 2, pp. 335–339, 2012. View at Google Scholar
  10. M. Mahmoud and P. Shi, “Asynchronous H filtering of discrete-time switched systems,” Signal Processing, vol. 92, no. 10, pp. 2356–2364, 2012. View at Google Scholar
  11. L. Zhang and P. Shi, “H filtering for a class of switched linear parameter varying systems,” International Journal of Systems Science, vol. 42, no. 5, pp. 781–788, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Yang, P. Shi, J. Zhang, and J. Qiu, “Robust H filtering for a class of Markovian jump systems with time-varying delays based on delta operator approach,” Asian Journal of Control, vol. 13, no. 3, pp. 398–407, 2011. View at Google Scholar
  13. B. Jiang, Z. Mao, and P. Shi, “H-filter design for a class of networked control systems via TS fuzzy-model approach,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 1, pp. 201–208, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Basin, P. Shi, and P. Soto, “Central suboptimal H filtering for nonlinear polynomial systems with multiplicative noise,” Journal of the Franklin Institute, vol. 347, no. 9, pp. 1740–1754, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. F. Li and X. Zhang, “Delay-range-dependent robust H 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
  16. M. Basin and J. Maldonado, “Mean-square filtering for incompletely measured polynomial states confused with poisson noises,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 10, pp. 6085–6096, 2011. View at Google Scholar
  17. G. Zong, L. Hou, and J. Li, “A descriptor system approach to L2L filtering for uncertain discrete-time switched system with mode-dependent time-varying delays,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 5 A, pp. 2213–2224, 2011. View at Google Scholar · View at Scopus
  18. J. Liu, Z. Gu, and S. Hu, “H filtering for Markovian jump systems with time-varying delays,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 3, pp. 1299–1310, 2011. View at Google Scholar · View at Scopus
  19. C. K. Ahn and M. K. Song, “L2L filtering for time-delayed switched hopfield neural networks,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 4, pp. 1831–1844, 2011. View at Google Scholar
  20. L. Ma, F. Da, and K. J. Zhang, “Exponential H filter design for discrete time-delay stochastic systems with markovian jump parameters and missing measurements,” IEEE Transactions on Circuits and Systems I, vol. 58, no. 5, pp. 994–1007, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. 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
  22. 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 Scopus
  23. Z. Wang, J. Lam, and X. Liu, “Filtering for a class of nonlinear discrete-time stochastic systems with state delays,” Journal of Computational and Applied Mathematics, vol. 201, no. 1, pp. 153–163, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. Y. Liu, Z. Wang, and X. Liu, “Robust H filtering for discrete nonlinear stochastic systems with time-varying delay,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 318–336, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. B. Shen, Z. Wang, H. Shu, and G. Wei, “H filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays,” Automatica, vol. 45, no. 4, pp. 1032–1037, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Niu, D. W. C. Ho, and C. W. Li, “Filtering for discrete fuzzy stochastic systems with sensor nonlinearities,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 971–978, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. H. Yan, H. Zhang, H. Shi, and M. Q. H. Meng, “H fuzzy filtering for discrete-time fuzzy stochastic systems with time-varying delay,” in Proceedings of the 29th Chinese Control Conference (CCC '10), pp. 5993–5998, July 2010. View at Scopus
  28. X. G. Guo and G. H. Yang, “Reliable H filter design for discrete-time systems with sector-bounded nonlinearities: an LMI optimization approach,” Zidonghua Xuebao/ Acta Automatica Sinica, vol. 35, no. 10, pp. 1347–1351, 2009. View at Publisher · View at Google Scholar · View at Scopus
  29. B. Zhou, W. Zheng, Y. Fu, and G. Duan, “H filtering for linear continuous-time systems subject to sensor non- linearities,” IET Control Theory Applications, vol. 5, no. 16, pp. 1925–1937, 2011. View at Google Scholar
  30. P. Shi, X. Luan, and F. Liu, “H filtering for discrete-time systems with stochastic incomplete measurement and mixed delays,” IEEE Transactions on Industrial Electronics, vol. 59, no. 6, pp. 2732–2739, 2012. View at Google Scholar
  31. M. Liu, S. Zhang, and S. Zheng, “New results on H filter design for time-delayed discrete-time system with nonlinear sensors,” in Proceedings of the 30th Chinese Control Conference, pp. 3078–3082, 2011.
  32. S. Suranthiran and S. Jayasuriya, “Optimal fusion of multiple nonlinear sensor data,” IEEE Sensors Journal, vol. 4, no. 5, pp. 651–663, 2004. View at Publisher · View at Google Scholar · View at Scopus