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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 750841, 16 pages
http://dx.doi.org/10.1155/2012/750841
Research Article

Robust / Filter Design for a Class of Nonlinear Stochastic Systems with State-Dependent Noise

1College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266590, China
2Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan
3College of Information and Control Engineering, China University of Petroleum (East China), Qingdao 266555, China

Received 17 June 2012; Accepted 24 August 2012

Academic Editor: Jun Hu

Copyright © 2012 Weihai Zhang 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. J. Grimble and A. Elsayed, “Solution of the H optimal linear filtering problem for discrete-time systems,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 7, pp. 1092–1104, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. W. M. McEneaney, “Robust/H filtering for nonlinear systems,” Systems & Control Letters, vol. 33, no. 5, pp. 315–325, 1998. View at Publisher · View at Google Scholar
  3. S. Xu, J. Lam, and Y. Zou, “H filtering for singular systems,” IEEE Transactions on Automatic Control, vol. 48, no. 12, pp. 2217–2222, 2003. View at Publisher · View at Google Scholar
  4. S. Xu, J. Lam, and X. Mao, “Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays,” IEEE Transactions on Circuits and Systems. I., vol. 54, no. 9, pp. 2070–2077, 2007. View at Publisher · View at Google Scholar
  5. Z. Wang, B. Shen, and X. Liu, “H filtering with randomly occurring sensor saturations and missing measurements,” Automatica, vol. 48, no. 3, pp. 556–562, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Z. Wang and B. Huang, “Robust H2/H filtering for linear systems with error variance constraints,” IEEE Transactions on Signal Processing, vol. 48, no. 8, pp. 2463–2467, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. Gao, J. Lam, L. Xie, and C. Wang, “New approach to mixed H2/H filtering for polytopic discrete-time systems,” IEEE Transactions on Signal Processing, vol. 53, no. 8, part 2, pp. 3183–3192, 2005. View at Publisher · View at Google Scholar
  8. B. S. Chen, C. L. Tsai, and Y. F. Chen, “Mixed H2/H filtering design in multirate transmultiplexer system LMI approach,” IEEE Transactions on Signal Processing, vol. 49, no. 11, pp. 2693–2701, 2001. View at Publisher · View at Google Scholar
  9. R. Z. Has'minskii, Stochastic Stability of Differential Equations, vol. 7, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
  10. 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
  11. D. Hinrichsen and A. J. Pritchard, “Stochastic H,” SIAM Journal on Control and Optimization, vol. 36, no. 5, pp. 1504–1538, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. E. Gershon, D. J. N. Limebeer, U. Shaked, and I. Yaesh, “Robust H filtering of stationary continuous-time linear systems with stochastic uncertainties,” IEEE Transactions on Automatic Control, vol. 46, no. 11, pp. 1788–1793, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. Xu and T. Chen, “Reduced-order H filtering for stochastic systems,” IEEE Transactions on Signal Processing, vol. 50, no. 12, pp. 2998–3007, 2002. View at Publisher · View at Google Scholar
  14. Z. Wang, Y. Liu, and X. Liu, “H filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities,” Automatica, vol. 44, no. 5, pp. 1268–1277, 2008. View at Publisher · View at Google Scholar
  15. 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, part 1, pp. 589–598, 2005. View at Publisher · View at Google Scholar
  16. W. Zhang, G. Feng, and Q. Li, “Robust H filtering for nonlinear stochastic state-delayed systems,” in Proceedings of the 7th World Congress on Intelligent Control and Automation (WCICA '08), pp. 2212–2217, Chongqing, China, June 2008.
  17. C. S. Tseng, “Robust fuzzy filter design for a class of nonlinear stochastic systems,” IEEE Transactions on Fuzzy Systems, vol. 152, pp. 261–274, 2007. View at Google Scholar
  18. B. Shen, Z. Wang, H. Shu, and G. Wei, “On nonlinear H filtering for discrete-time stochastic systems with missing measurements,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2170–2180, 2008. View at Publisher · View at Google Scholar
  19. H. Dong, Z. Wang, and H. Gao, “Robust H filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts,” IEEE Transactions on Signal Processing, vol. 58, no. 4, pp. 1957–1966, 2010. View at Publisher · View at Google Scholar
  20. 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
  21. B. Øksendal, Stochastic Differential Equations, Springer, Berlin, Germany, 5th edition, 1998.
  22. W. M. Wonham, “Random differential equations in control theory,” in Probabilistic Methods in Applied Mathematics, vol. 2, pp. 131–212, Academic Press, New York, NY, USA, 1970. View at Google Scholar · View at Zentralblatt MATH
  23. W. Zhang and B.-S. Chen, “On stabilizability and exact observability of stochastic systems with their applications,” Automatica, vol. 40, no. 1, pp. 87–94, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. V. Drăgan, T. Morozan, and A. Halanay, “Optimal stabilizing compensator for linear systems with state-dependent noise,” Stochastic Analysis and Applications, vol. 10, no. 5, pp. 557–572, 1992. View at Publisher · View at Google Scholar