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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 979878, 8 pages
http://dx.doi.org/10.1155/2013/979878
Research Article

Robust Filtering for Takagi-Sugeno Fuzzy Systems with Norm-Bounded Uncertainties

College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, Zhejiang 325035, China

Received 13 November 2012; Accepted 4 March 2013

Academic Editor: Antonia Vecchio

Copyright © 2013 Wenbai Li 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. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, no. 1, pp. 116–132, 1985.
  2. J. hun Kim, C.-H. Hyun, E. Kim, and M. Park, “Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 359–369, 2007.
  3. B. Castillo-Toledo and J. A. Meda-Campaña, “The fuzzy discrete-time robust regulation problem: an LMI approach,” IEEE Transactions on Fuzzy Systems, vol. 12, no. 3, pp. 360–367, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. T.-H. Li and K.-J. Lin, “Composite fuzzy control of nonlinear singularly perturbed systems,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 176–187, 2007. View at Publisher · View at Google Scholar
  5. M. Chadli and T. Guerra, “LMI solution for robust static output feedback control of discrete Takagi-Sugeno fuzzy models,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 6, pp. 1160–1165, 2012. View at Publisher · View at Google Scholar
  6. T. Zhang, G. Feng, H. Liu, and J. Lu, “Piecewise fuzzy anti-windup dynamic output feedback control of nonlinear processes with amplitude and rate actuator saturations,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 2, pp. 253–264, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. J.-C. Lo and M.-L. Lin, “Observer-based robust H control for fuzzy systems using two-step procedure,” IEEE Transactions on Fuzzy Systems, vol. 12, no. 3, pp. 350–359, 2004.
  8. H.-N. Wu and H.-Y. Zhang, “Reliable H fuzzy control for continuous-time nonlinear systems with actuator failures,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 5, pp. 609–618, 2006. View at Publisher · View at Google Scholar
  9. K. Tanaka and H. O. Wang, Fuzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, Wiley, New York, NY, USA, 2001.
  10. 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
  11. H. H. Choi, “Robust stabilization of uncertain fuzzy-time-delay systems using sliding-mode-control approach,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 979–984, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. B.-S. Chen and C.-H. Wu, “Robust optimal reference-tracking design method for stochastic synthetic biology systems: T-S fuzzy approach,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 6, pp. 1144–1159, 2010.
  13. S. H. Kim and P. Park, “H state-feedback-control design for discrete-time fuzzy systems using relaxation technique for parameterized LMI,” IEEE Transactions on Fuzzy Systems, vol. 18, no. 5, pp. 985–993, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Zhang, Y. Shi, and A. Saadat Mehr, “On H filtering for discrete-time Takagi-Sugeno fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 2, pp. 396–401, 2012.
  15. B. Chen and X. Liu, “Delay-dependent robust H control for T-S fuzzy systems with time delay,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 4, pp. 544–556, 2005.
  16. D. H. Lee, J. B. Park, and Y. H. Joo, “A new fuzzy lyapunov function for relaxed stability condition of continuous-time Takagi-Sugeno fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 4, pp. 785–791, 2011.
  17. H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, “Parameterized linear matrix inequality techniques in fuzzy control system design,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 2, pp. 324–332, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. H. Liu, F. Sun, and Z. Sun, “Stability analysis and synthesis of fuzzy singularly perturbed systems,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 273–284, 2005.
  19. X.-H. Chang, “Robust nonfragile H filtering of fuzzy systems with linear fractional parametric uncertainties,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 6, pp. 1001–1011, 2012.
  20. B. Chen and X. Liu, “Fuzzy guaranteed cost control for nonlinear systems with time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 238–249, 2005.
  21. H. H. Choi, “Robust stabilization of uncertain fuzzy systems using variable structure system approach,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 3, pp. 715–724, 2008.
  22. K.-Y. Lian and J.-J. Liou, “Output tracking control for fuzzy systems via output feedback design,” IEEE Transactions on Fuzzy Systems, vol. 14, no. 5, pp. 628–639, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. W.-H. Ho, J.-T. Tsai, and J.-H. Chou, “Robust quadratic-optimal control of TS-fuzzy-model-based dynamic systems with both elemental parametric uncertainties and norm-bounded approximation error,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 518–531, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. G. Feng, M. Chen, D. Sun, and T. Zhang, “Approaches to robust filtering design of discrete time fuzzy dynamic systems,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 2, pp. 331–340, 2008. View at Publisher · View at Google Scholar
  25. M. Chen, G. Feng, H. Ma, and G. Chen, “Delay-dependent H filter design for discrete-time fuzzy systems with timevarying delays,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 604–616, 2009.
  26. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Fluids Engineering, vol. 82, no. 1, pp. 35–45, 1960. View at Publisher · View at Google Scholar
  27. H. Zhang and X. Xie, “Relaxed stability conditions for continuous-time TS fuzzy-control systems via augmented multi-indexed matrix approach,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 3, pp. 478–492, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. T. Guerra, H. Kerkeni, J. Lauber, and L. Vermeiren, “An efficient lyapunov function for discrete T-S models: observer design,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 1, pp. 187–192, 2012.
  29. S. He and F. Liu, “Finite-time H fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 605–614, 2012.
  30. H. Zhang, Y. Shi, and A. Saadat Mehr, “Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data,” IET Control Theory and Applications, vol. 4, no. 12, pp. 2921–2936, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. J. An, G. Wen, C. Lin, and R. Li, “New results on a delay-derivative-dependent fuzzy H filter design for T-S fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 4, pp. 770–779, 2011.
  32. A. P. C. Gonçalves, A. R. Fioravanti, and J. C. Geromel, “H filtering of discrete-time Markov jump linear systems through linear matrix inequalities,” IEEE Transactions on Automatic Control, vol. 54, no. 6, pp. 1347–1351, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  33. H. Zhang, A. S. Mehr, and Y. Shi, “Improved robust energy-to-peak filtering for uncertain linear systems,” Signal Processing, vol. 90, no. 9, pp. 2667–2675, 2010. View at Publisher · View at Google Scholar · View at Scopus
  34. R. Yang, H. Gao, and P. Shi, “Delay-dependent l2l filter design for stochastic time-delay systems,” IET Control Theory and Applications, vol. 5, no. 1, pp. 1–8, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. M. S. Mahmoud, “Resilient l2l filtering of polytopic systems with state delays,” IET Control Theory & Applications, vol. 1, no. 1, pp. 141–154, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  36. 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
  37. J. Qiu, G. Feng, and J. Yang, “New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay,” IET Control Theory and Applications, vol. 2, no. 9, pp. 795–806, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. M. C. de Oliveira, “Investigating duality on stability conditions,” Systems & Control Letters, vol. 52, no. 1, pp. 1–6, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. G. Garcia, J. Bernussou, and D. Arzelier, “Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty,” Systems and Control Letters, vol. 22, no. 5, pp. 327–339, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. L. Yuan, “Robust analysis and synthesis of linear time-delay systems with norm-bounded time-varying uncertainty,” Systems & Control Letters, vol. 28, no. 5, pp. 281–289, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet