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Static output feedback control for continuous-time T-S fuzzy systems: An LMI approach

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Abstract

This paper presents a design method of static output feedback control for continuous-time T-S fuzzy systems. Based on parallel distributed compensation (PDC), a static output feedback control is utilized. A new sufficient condition for the existence of static output feedback gains is represented in terms of linear matrix inequalities (LMIs). The sufficient condition does not need any transformation matrices, equality constraints, and block diagonal assumption of positive definite matrices in order to convert a bilinear matrix inequality (BMI) problem to an LMI one.

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References

  1. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., vol. 15, no. 1, pp. 116–132, 1985.

    Article  MATH  Google Scholar 

  2. H. Wang, K. Tanaka, and M. Griffin, “Parallel distributed compensation of nonlinear systems by Takagi and Sugeno’s fuzzy model,” Proc. FUZZIEEE, Yokohama, Japan, pp. 531–538, 1995.

    Google Scholar 

  3. H. O. Wang, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: Stability and design issues,” IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14–23, February 1996.

    Article  Google Scholar 

  4. V. L. Syrmos, C. T. Abdallah, P. Dorato, and K. Grigoriadis, “Static output feedback — a survey,” Automatica, vol. 33, no. 2, pp. 125–137, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. C. Geromel, C. C. de Souza, and R. E. Skelton, “Static output feedback controllers: stability and convexity,” IEEE Trans. Automat. Contr., vol. 43, no. 1, pp. 120–125, 1998.

    Article  MATH  Google Scholar 

  6. Y.-Y. Cao, J. Lam, and Y.-X. Sun, “Static output feedback stabilization: an ILMI approach,” Automatica, vol. 34, no. 12, pp. 1641–1645, 1998.

    Article  MATH  Google Scholar 

  7. L. E. Ghaoui, F. Oustry, and M. Ait Rami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Trans. Automat. Contr., vol. 42, no. 8, August 1997.

    Google Scholar 

  8. H.-N. Wu, “An ILMI approach to robust H 2 static output feedback fuzzy control for uncertain discrete-time nonlinear systems,” Automatica, vol. 44, pp. 2333–2339, 2008.

    Article  MATH  Google Scholar 

  9. D. Huang and S. K. Nguang, “Robust H ∞ static output feedback control of fuzzy systems: an ILMI approach”, IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 36, no. 1, pp. 216–222, February 2006.

    Article  Google Scholar 

  10. M. Nachidi, A. Benzaouia, F. Tadeo, and M. A. Rami, “LMI_based approach for output-feedback stabilization for discrete-time Takagi-Sugeno systems,” IEEE Trans. Fuzzy Syst., vol. 16, no. 5, pp. 1188–1196, October 2008.

    Article  Google Scholar 

  11. J.-C. Lo and M.-L. Lin, “Robust H ∞ nonlinear control via fuzzy static output feedback,” IEEE Trans. Circuits and Systems-1: Fundamental Theory and Applications, vol. 50, no. 11, pp. 1494–1502, 2003.

    Article  MathSciNet  Google Scholar 

  12. C. A. R. Crusius and A. Trofino, “Sufficient LMI conditions for output feedback control problems,” IEEE Trans. Automatic Control, vol. 44, no. 4, pp. 1053–1057, May 1999.

    Article  MATH  MathSciNet  Google Scholar 

  13. W. Chang, J. B. Park, Y. H. Joo, and G. Chen, “Static output-feedback fuzzy controller for Chen’s chaotic system with uncertainties,” Information Sciences, vol. 151, pp. 227–244, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Soliman, A. L. Elshafei, F. Bendary, and W. Mansour, “LMI static output-feedback design of fuzzy power system stabilizers,” Expert Systems with Applications, vol. 36, pp. 6817–6825, 2009.

    Article  Google Scholar 

  15. C.-H. Fang, Y.-S. Liu, S.-W. Kau, L. Hong, and C.-H. Lee, “A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems,” IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 386–397, June 2006.

    Article  Google Scholar 

  16. 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, pp. 135–146, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. J. Lee and D. W. Kim, “Robust stabilization of T-S fuzzy systems: fuzzy static output feedback under parametric uncertainty,” Int. J. Control, Automation, and Systems, vol. 7, no. 5, pp. 731–736, 2009.

    Article  Google Scholar 

  18. G. B. Koo, J. B. Park, and Y. H. Joo, “Robust fuzzy controller for Large-scale nonlinear systems using decentralized static output feedback,” Int. J. Control, Automation, and Systems, vol. 9, no. 4, pp. 649–658, 2011.

    Article  Google Scholar 

  19. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994.

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Control and Instrumentation Engineering, Changwon National University, 9 Sarimdong, Uichang-gu, Changwon, Geoysangnam-do, 641-773, Korea

    Eun Tae Jeung

  2. Department of Information & Communication, Pyeongtaek University, 111 Yongyi-dong, Pyeongtaek, Kyungki-do, 450-701, Korea

    Kap Rai Lee

Authors
  1. Eun Tae Jeung
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  2. Kap Rai Lee
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Correspondence to Eun Tae Jeung.

Additional information

Recommended by Associate Editor Do Wan Kim under the direction of Editor Young-Hoon Joo.

This research is financially supported by Changwon National University in 2013-2014.

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Jeung, E.T., Lee, K.R. Static output feedback control for continuous-time T-S fuzzy systems: An LMI approach. Int. J. Control Autom. Syst. 12, 703–708 (2014). https://doi.org/10.1007/s12555-013-0427-8

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  • DOI: https://doi.org/10.1007/s12555-013-0427-8

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