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Mathematical Problems in Engineering
Volume 2015, Article ID 734934, 9 pages
http://dx.doi.org/10.1155/2015/734934
Research Article

Piecewise Static Output Feedback Controller Design for Nonlinear Systems Based on T-S Affine Fuzzy Models

State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China

Received 23 October 2014; Accepted 27 January 2015

Academic Editor: Hak-Keung Lam

Copyright © 2015 Xingang Zhao. 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. View at Publisher · View at Google Scholar · View at Scopus
  2. T. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequlity Approach, John Wiley & Sons, New York, NY, USA, 2001.
  3. S. G. Cao, N. W. Rees, and G. Feng, “Analysis and design for a class of complex control systems. I. Fuzzy modelling and identification,” Automatica, vol. 33, no. 6, pp. 1017–1028, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Sala and C. Ariño, “Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya's theorem,” Fuzzy Sets and Systems, vol. 158, no. 24, pp. 2671–2686, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. Kruszewski, R. Wang, and T. M. Guerra, “Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: a new approach,” IEEE Transactions on Automatic Control, vol. 53, no. 2, pp. 606–611, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. X. Xie, D. Yue, T. Ma, and X. Zhu, “Further studies on control synthesis of discrete-time T-S Fuzzy systems via augmented multi-indexed matrix approach,” IEEE Transactions on Cybernetics, vol. 44, no. 12, pp. 2784–2791, 2014. View at Publisher · View at Google Scholar · View at Scopus
  7. H. K. Lam and S.-H. Tsai, “Stability analysis of polynomial-fuzzy-model-based control systems with mismatched premise membership functions,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 223–229, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Q. Shen and D. Ye, “Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions,” Fuzzy Sets and Systems, vol. 217, pp. 80–95, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Q. Gao, X.-J. Zeng, G. Feng, Y. Wang, and J. B. Qiu, “T-S-fuzzy-model-based approximation and controller design for general nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 42, no. 4, pp. 1143–1154, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Wang, L.-Y. Peng, H.-H. Ju, and Y.-L. Wang, “H state feedback controller design for continuous-time T-S fuzzy systems in finite frequency domain,” Information Sciences, vol. 223, pp. 221–235, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Wang and J. Fei, “Robust adaptive sliding mode control of MEMS gyroscope using T-S fuzzy model,” Nonlinear Dynamics, vol. 77, no. 1-2, pp. 361–371, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. E. Kim and S. Kim, “Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: continuous case,” IEEE Transactions on Fuzzy Systems, vol. 10, no. 3, pp. 391–400, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. C. Fantuzzi and R. Rovatti, “On the approximation capabilities of the homogeneous Takagi-Sugeno model,” in Proceedings of the 5th IEEE International Conference on Fuzzy Systems, pp. 1067–1072, New Orleans, La, USA, September 1996. View at Scopus
  14. H. Wang and G.-H. Yang, “Piecewise controller design for affine fuzzy systems via dilated linear matrix inequality characterizations,” ISA Transactions, vol. 51, no. 6, pp. 771–777, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. Shu, J. Lam, and J. Xiong, “Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach,” Automatica, vol. 46, no. 4, pp. 687–694, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. S. W. Yun, Y. J. Choi, and P. Park, “Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization,” Nonlinear Dynamics, vol. 62, no. 1-2, pp. 95–104, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. D. Huang and S. K. Nguang, “Robust H static output feedback control of fuzzy systems: an ILMI approach,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 36, no. 1, pp. 216–222, 2006. View at Google Scholar
  18. H.-N. Wu, “An ILMI approach to robust H2 static output feedback fuzzy control for uncertain discrete-time nonlinear systems,” Automatica, vol. 44, no. 9, pp. 2333–2339, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. Q. Ma, “Robust H2/H static output feedback control for uncertain discretetime fuzzy systems,” in Proceedings of the International Conference on Intelligent System Design and Engineering Application (ISDEA '10), pp. 326–329, 2010.
  20. Y. C. Chang, S. S. Chen, S. F. Su, and T. T. Lee, “Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 148, no. 3, pp. 395–410, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. S.-W. Kau, H.-J. Lee, C.-M. Yang, C.-H. Lee, L. Hong, and C.-H. Fang, “Robust H fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties,” Fuzzy Sets and Systems, vol. 158, no. 2, pp. 135–146, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C.-S. Chiu and T.-S. Chiang, “Robust output regulation of T-S fuzzy systems with multiple time-varying state and input delays,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 4, pp. 962–975, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Dong and G.-H. Yang, “Static output feedback H control of a class of nonlinear discrete-time systems,” Fuzzy Sets and Systems, vol. 160, no. 19, pp. 2844–2859, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. E. Kim, C. H. Lee, and Y. W. Cho, “Analysis and design of an affine fuzzy system via bilinear matrix inequality,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 115–123, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. J. B. Qiu, G. Feng, and H. J. Gao, “Asynchronous output-feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model-based approach,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 6, pp. 1014–1030, 2011. View at Publisher · View at Google Scholar · View at Scopus