Robust Fuzzy Feedback Linearization Control Based on Takagi-Sugeno Fuzzy Models

  • Published : 2002.12.01


In this paper, well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model and uncertainty is assumed to be included in the model structure with known bounds. Based on the fuzzy models, a numerical robust stability analysis for the fuzzy feedback linearization regulator is presented using Linear Matrix Inequalities (LMI) Theory. For these structured uncertainty, the closed system can be cast into Lur'e system by simple transformation. From the LMI stability condition for Lur'e system, we can derive the robust stability condition for the fuzzy feedback linearization regulator based on Takagi-Sugeno fuzzy model. The effectiveness of the proposed analysis is illustrated by a simple example.


  1. Applied nonlinear Control J. E. Slotine;W. Li
  2. Nonlinear control systems A. Isidori
  3. Fuzzy control M. Sugeno
  4. Adaptive fuzzy systems and control: design and stability analysis L. Wang
  5. IEEE Trans. Fuzzy Systems v.4 no.1 H$^{\infty}$ tracking design of uncertain nonlinear SISO systems : adaptive fuzzy approach B. S. Chen;C. H. Lee;Y. C. Chang
  6. IEEE Trans. Fuzzy Systems v.7 no.1 An improved stable adaptive fuzzy control method K. Fischle;D. Schroder
  7. IEEE Trans. Fuzzy Systems v.7 no.2 The adaptive control of nonlinear systems using the Sugeno-type of fuzzy logic D. L. Tsay;H. Y. Chung;C. J.Lee
  8. IEEE Trans. Fuzzy Systems v.6 no.4 Robust stability analysis and design method for the fuzzy feedback linearization regulator H. J. Kang;C. Kwon;C. H. Lee;M. Park
  9. IEEE Trans. Syst., Man, Cybern v.15 no.1 Fuzzy Identification of systems and its applications to modeling and control T. Takagi;M. Sugeno
  10. Linear matrix inequalities in systems and control theory S. Boyd
  11. Interior-point polynomial methods in convex programming Y. Nesterov;A. Nemirovsky
  12. IEEE Trans. Fuzzy Systems v.4 no.1 An approach to fuzzy control of nonlinear system: stability and design issues H. O. Wang;K. Tanaka;F. G. Grifiin
  13. IEEE Trans. Fuzzy Systems v.4 no.1 Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H$^{\infty}$ control theory, and linear matrix inequalities K. Tanaka;T. lkeda;H. O. Wang
  14. FUZZ-IEEE'1999 A new PDC for fuzzy reference models T. Taniguchi;K. Tanaka;K. Yamafugi;H. O. Wang
  15. FUZZ-IEEE'1999 An improved stability analysis and design of fuzzy control systems H. K. Lam;F. H. F. Leung;P. K. S. Tam
  16. IEEE Trans. Fuzzy Systems v.29 no.4 Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities E. Kim;H. J. Kang;M. Park
  17. Some Nonlinear problems in the theory of automatic control Lur'e, A. I
  18. LMI Control Toolbox P. Gahinet;A.Nemirovski;A. Laub;M. Chilali
  19. IEEE Trans. Automat. Contr. v.44 no.1 Robust H$^{\infty}$ control for linear discrete-time systems with norm-bounded nonlinear uncertainties P. Shi;S. P. Shue
  20. Nonlinear system analysis M. Vidyasagar