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Mathematical Problems in Engineering
Volume 2015, Article ID 453806, 8 pages
http://dx.doi.org/10.1155/2015/453806
Research Article

State Estimation for Discrete-Time Takagi-Sugeno Fuzzy Systems with Time-Varying Delays

1Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China
2School of Management, Chongqing Jiaotong University, Chongqing 400074, China
3Department of Mathematics, Yangzhou University, Yangzhou 225002, China
4Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 25 August 2014; Accepted 10 September 2014

Academic Editor: Zidong Wang

Copyright © 2015 Ting Lei 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. 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 Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. Z. Wang, H. Dong, B. Shen, and H. Gao, “Finite-horizon H filtering with missing measurements and quantization effects,” IEEE Transactions on Automatic Control, vol. 58, no. 7, pp. 1707–1718, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. G. Feng, “A survey on analysis and design of model-based fuzzy control systems,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 5, pp. 676–697, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Lin, Q.-G. Wang, T. H. Lee, Y. He, and B. Chen, “Observer-based fuzzy control design for T-S fuzzy systems with state delays,” Automatica, vol. 44, no. 3, pp. 868–874, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. H. Dong, Z. Wang, and H. Gao, “Distributed H filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. Y. Li and X. Zhou, “T-S fuzzy model-based approximation and filter design for stochastic time-delay systems with Hankel norm criterion,” Abstract and Applied Analysis, vol. 2014, Article ID 937495, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. H. K. Lam, “Stability analysis of T-S fuzzy control systems using parameter-dependent Lyapunov function,” IET Control Theory & Applications, vol. 3, no. 6, pp. 750–762, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Z. Yang and Y.-P. Yang, “New delay-dependent stability analysis and synthesis of T-S fuzzy systems with time-varying delay,” International Journal of Robust and Nonlinear Control, vol. 20, no. 3, pp. 313–322, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. C. Peng, L.-Y. Wen, and J.-Q. Yang, “On delay-dependent robust stability criteria for uncertain T-S fuzzy systems with interval time-varying delay,” International Journal of Fuzzy Systems, vol. 13, no. 1, pp. 35–44, 2011. View at Google Scholar · View at MathSciNet · View at Scopus
  10. S. Lakshmanan, R. Rakkiyappan, and P. Balasubramaniam, “Global robust stability criteria for T-S fuzzy systems with distributed delays and time delay in the leakage term,” Iranian Journal of Fuzzy Systems, vol. 9, no. 2, pp. 127–146, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Xing, Q. Zhang, and Y. Zhang, “Finite-time stability analysis and control for a class of stochastic singular biological economic systems based on T-S fuzzy model,” Abstract and Applied Analysis, vol. 2013, Article ID 946491, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. F. Ahmida and E. H. Tissir, “Exponential stability of uncertain T-S fuzzy switched systems with time delay,” International Journal of Automation and Computing, vol. 10, no. 1, pp. 32–38, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. H.-B. Zeng, J. H. Park, J.-W. Xia, and S.-P. Xiao, “Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay,” Applied Mathematics and Computation, vol. 235, pp. 492–501, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. Y. Mao and H. Zhang, “Exponential stability and robust H control of a class of discrete-time switched non-linear systems with time-varying delays via T-S fuzzy model,” International Journal of Systems Science, vol. 45, no. 5, pp. 1112–1127, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. X. Yang, L. Wu, H.-K. Lam, and X. Su, “Stability and stabilization of discrete-time T-S fuzzy systems with stochastic perturbation and time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 124–138, 2014. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Ahn and P. Kim, “T-S fuzzy adaptive delayed feedback synchronization for time-delayed chaotic systems with uncertain parameters,” International Journal of Modern Physics B, vol. 25, no. 23-24, pp. 3253–3267, 2011. View at Google Scholar
  17. X. Wu, Y. Wang, X. Dang, and L. Huang, “Adaptive synchronization of T-S fuzzy complex networks with time-varying delays via the pinning control method,” Nonlinear Dynamics, vol. 74, no. 1-2, pp. 143–152, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. D. Xu, W. Gui, P. Zhao, and C. Yang, “Hybrid synchronization of general T-S fuzzy complex dynamical networks with time-varying delay,” Mathematical Problems in Engineering, vol. 2013, Article ID 384654, 8 pages, 2013. View at Publisher · View at Google Scholar
  19. F.-H. Hsiao, “Optimal exponential synchronization of chaotic systems with multiple time delays via fuzzy control,” Abstract and Applied Analysis, vol. 2013, Article ID 742821, 19 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Liang, Z. Wang, and X. Liu, “Robust passivity and passification of stochastic fuzzy time-delay systems,” Information Sciences, vol. 180, no. 9, pp. 1725–1737, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Liang, Z. Wang, and X. Liu, “On passivity and passification of stochastic fuzzy systems with delays: the discrete-time case,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 40, no. 3, pp. 964–969, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. B. Zhang, W. X. Zheng, and S. Xu, “Passivity analysis and passive control of fuzzy systems with time-varying delays,” Fuzzy Sets and Systems, vol. 174, no. 1, pp. 83–98, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  23. C. Han, L. Wu, P. Shi, and Q. Zeng, “Passivity and passification of T-S fuzzy descriptor systems with stochastic perturbation and time delay,” IET Control Theory & Applications, vol. 7, no. 13, pp. 1711–1724, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. T. Lei, Z. Chen, Q. Song, and Z. Zhao, “Passivity analysis and passive control for T-S fuzzy systems with leakage delay and mixed time-varying delays,” Abstract and Applied Analysis, vol. 2013, Article ID 524028, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  25. Q. Song, Z. Wang, and J. Liang, “Analysis on passivity and passification of T-S fuzzy systems with time-varying delays,” Journal of Intelligent and Fuzzy Systems, vol. 24, no. 1, pp. 21–30, 2013. View at Publisher · View at Google Scholar · View at Scopus
  26. Q. Song, Z. Zhao, and J. Yang, “Passivity and passification for stochastic Takagi-Sugeno fuzzy systems with mixed time-varying delays,” Neurocomputing, vol. 122, pp. 330–337, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. T. Lei, Q. Song, and Z. Zhao, “Further result on passivity for discrete-time stochastic T-S fuzzy systems with time-varying delays,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 657621, 8 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Ding, Z. Wang, H. Dong, and H. Shu, “Distributed H state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case,” Automatica, vol. 48, no. 8, pp. 1575–1585, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. B. Shen, Z. Wang, D. Ding, and H. Shu, “H state estimation for complex networks with uncertain inner coupling and incomplete measurements,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 12, pp. 2027–2037, 2013. View at Publisher · View at Google Scholar · View at Scopus
  30. B.-K. Lee, K.-H. Lee, and B.-S. Chen, “State estimation of stochastic T-S fuzzy systems,” International Journal of Fuzzy Systems, vol. 8, no. 1, pp. 46–56, 2006. View at Google Scholar · View at Scopus
  31. Z. Gao, X. Shi, and S. X. Ding, “Fuzzy state/disturbance observer design for T-S fuzzy systems with application to sensor fault estimation,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 38, no. 3, pp. 875–880, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. J. Qiu, G. Feng, and H. Gao, “Nonsynchronized-State estimation of multichannel networked nonlinear systems with multiple packet dropouts Via TS Fuzzy-Affine dynamic models,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 1, pp. 75–90, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. K. Salahshoor and M. F. Samadi, “A novel fuzzy approach for state estimation of nonlinear hybrid systems,” Asian Journal of Control, vol. 14, no. 4, pp. 974–990, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. X. Li and R. Rakkiyappan, “Robust asymptotic state estimation of Takagi-Sugeno fuzzy Markovian jumping Hopfield neural networks with mixed interval time-varying delays,” Mathematical Methods in the Applied Sciences, vol. 34, no. 17, pp. 2197–2207, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  35. C. K. Ahn, “State estimation for T-S fuzzy Hopfield neural networks via strict output passivation of the error system,” International Journal of General Systems, vol. 42, no. 5, pp. 503–518, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. D. Zhang, W. Cai, and Q.-G. Wang, “Mixed H and passivity based state estimation for fuzzy neural networks with Markovian-type estimator gain change,” Neurocomputing, vol. 139, pp. 321–327, 2014. View at Publisher · View at Google Scholar · View at Scopus
  37. J. Carlos González-Castolo and E. López-Mellado, “Fuzzy state estimation of discrete event systems,” in MICAI 2006: Advances in Artificial Intelligence, vol. 4293 of Lecture Notes in Computer Science, pp. 90–100, 2006. View at Publisher · View at Google Scholar
  38. O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “New criteria on delay-dependent stability for discrete-time neural networks with time-varying delays,” Neurocomputing, vol. 121, pp. 185–194, 2013. View at Publisher · View at Google Scholar · View at Scopus