International Journal of Fuzzy Logic and Intelligent Systems

  • 제12권3호
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  • Pages.187-192
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  • 2012
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  • 1598-2645(pISSN)
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  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
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Controller Design for Continuous-Time Takagi-Sugeno Fuzzy Systems with Fuzzy Lyapunov Functions : LMI Approach

  • Kim, Ho-Jun (Department of Electrical and Electronic Eng., Yonsei Univ.) ;
  • Joo, Young-Hoon (Department of Control and Robotics Eng., Kunsan National Univ.) ;
  • Park, Jin-Bae (Department of Electrical and Electronic Eng., Yonsei Univ.)
  • 투고 : 2012.06.20
  • 심사 : 2012.09.24
  • 발행 : 2012.09.25
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초록

This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI Toolbox. Simulation examples are given to illustrate the effectiveness of this method.

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참고문헌

  1. K. Tanaka, and M. Segeno, "Stability analysis and design of fuzzy control of nonlinear systems: Stability and the design issues," Fuzzy Sets Syst., vol. 45, np. 2, pp. 1697-1700, 1992.
  2. E. T. Kim, and H. J Lee, "New approaches to relaxed quadratic stability conditions of fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 523-534, 2000. https://doi.org/10.1109/91.873576
  3. A. Sala, and C. Arino, "Relaxed stability and performance LMI conditions for Takagi-Sugeno fuzzy systems with polynomial constraints on membership function shapes," IEEE Trans. Fuzzy Syst., vol. 16, no. 5, pp.1328-1336, 2008. https://doi.org/10.1109/TFUZZ.2008.926585
  4. H. K. Lam, "LMI-based stability analysis for fuzzymodel- based control systems using artificial T-S fuzzy model," IEEE Trans. Fuzzy Syst., vol. 19, no. 3, pp. 505-513, 2011. https://doi.org/10.1109/TFUZZ.2011.2116027
  5. H. K. Lam and M. Narimani, "Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 949-961, 2009. https://doi.org/10.1109/TFUZZ.2008.928600
  6. T. M. Guerra, and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form," Automatica, vol. 40, no. 5 pp. 823-829, 2004.
  7. K. Tanaka, T. Hori, and H. O. Wang, "A multiple lyapunov function approach to stabilization of fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 582-589, 2003. https://doi.org/10.1109/TFUZZ.2003.814861
  8. 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 Trans. Fuzzy Syst., vol. 19, no. 4, pp. 785-791, 2011. https://doi.org/10.1109/TFUZZ.2011.2142315
  9. L. A. Mozelli, R. M. Palhares, and G. S. C. Avellar, "A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems," Information Science., vol. 179, no. 8, pp. 1149-1162, 2009. https://doi.org/10.1016/j.ins.2008.12.002
  10. Gahinet, P., Nemirovski, A., Laub., A. J., and Chilali, M. (1995), "LMI control toolbox. MathWorks,", Natick, Massachusetts.