Advertisement

T–S Fuzzy Systems

  • Ruiyun Qi
  • Gang Tao
  • Bin Jiang
Chapter
Part of the Communications and Control Engineering book series (CCE)

Abstract

This chapter presents an overview of ideas and techniques of Takagi–Sugeno (T–S) fuzzy systems. In Chap.  1, we have introduced the basic concepts of fuzzy sets, fuzzy logic, and fuzzy inference mechanism. This chapter aims to present a necessarily selective review on T–S fuzzy systems including their architectures, important properties, and applicability in the field of nonlinear system identification and control with particular emphasis on the issues which are directly related to the main topics addressed in the following chapters.

References

  1. Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in systems and control theory. SIAM, PA, PhiladelphiaGoogle Scholar
  2. Bronshtein IN, Semendyayev KA (1985) Handbook of mathematics. Van Nostrand Reinhold, New YorkzbMATHGoogle Scholar
  3. Buckley JJ (1993) Sugeno type controllers are universal controllers. Fuzzy Sets Syst 53:299–303MathSciNetCrossRefGoogle Scholar
  4. Cao SG, Rees NW, Feng G (1995) Analysis and design of fuzzy control systems using dynamic fuzzy global models. Fuzzy Sets Syst 75:47–62MathSciNetCrossRefGoogle Scholar
  5. Cao SG, Rees NW, Feng G (1997a) Analysis and design for a class of complex control systems - Part I: fuzzy modeling and identification. Automatica 33:1017–1028CrossRefGoogle Scholar
  6. Castro JL (1995) Fuzzy logic controllers are universal approximators. IEEE Trans Syst Man Cybern 25:629–635CrossRefGoogle Scholar
  7. Castro JL, Delgado M (1996) Fuzzy systems with defuzzification are universal approximators. IEEE Trans Syst Man Cybern 26:149–152CrossRefGoogle Scholar
  8. Chadli M, Maquin D, Ragot J (2000) Relaxed stability conditions for Takagi–Sugeno fuzzy systems. In: Proceedings of IEEE international conference on systems, man, and cybernetics, Nashville, TN, pp 3514–3519Google Scholar
  9. Chou J-H, Chen S-H (2001) Stability analysis of the discrete Takagi–Sugeno fuzzy model with time-varying consequent uncertainties. Fuzzy Sets Syst 118:271–279MathSciNetCrossRefGoogle Scholar
  10. Feng G (2004) Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans Fuzzy Syst 12(1):22–28CrossRefGoogle Scholar
  11. Feng G (2010) Analysis and synthesis of fuzzy control systems: a model-based approach. CRC Press, Boca RatonzbMATHGoogle Scholar
  12. Gahinet P, Nemirovski A, Laub AJ, Chilali M (1995) LMI control toolbox for use with Matlab. The Mathworks, MA, NatickGoogle Scholar
  13. Isidori A (1995) Nonlinear control systems, 3rd edn. Springer-Verlag, LondonCrossRefGoogle Scholar
  14. Jin Y (2003) Advanced fuzzy systems design and applications. Physica-Verlag, HeidelbergCrossRefGoogle Scholar
  15. Joh J, Chen YH, Langari R (1998) On the stability issues of linear Takagi-Sugeno fuzzy models. IEEE Trans Fuzzy Syst 6:402–410Google Scholar
  16. Johansson M, Rantzer A, Årzé K-E (1999) Piecewise quadratic stability of fuzzy systems. IEEE Trans Fuzzy Syst 7(6):713–722CrossRefGoogle Scholar
  17. Khalil HK (2002) Nonlinear systems. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar
  18. Kim E, Kim D (2001) Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: discrete case. IEEE Trans Syst Man Cybern 31:132–140Google Scholar
  19. Krstić M, Kanellakopoulos I, Kokotović P (1995) Nonlinear and adaptive control design. Wiley, New YorkzbMATHGoogle Scholar
  20. Lilly JH (2010) Fuzzy control and identification. Wiley, HobokenCrossRefGoogle Scholar
  21. Li N, Li SY (2004) Stability analysis and design of T-S fuzzy control system with simplified linear rule consequent. IEEE Trans Syst Man Cybern 34:788–795CrossRefGoogle Scholar
  22. Marino R, Tome P (1995) Nonlinear control design: geometric, adaptive and robust. Prentice-Hall, Englewood CliffsGoogle Scholar
  23. Nijmeijer H, Van der Schaft A (1990) Nonlinear dynamical control systems. Spring-Verlag, New YorkCrossRefGoogle Scholar
  24. Passino KM, Yurkovich S (1998) Fuzzy control. Addison Wesley Longman Inc., ReadingGoogle Scholar
  25. Rovatti R (1998) Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in Sobolev norms. IEEE Trans Fuzzy Syst 6:235–249CrossRefGoogle Scholar
  26. Tanaka K, Sano M (1994) A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer. IEEE Trans Fuzzy Syst 2(2):119–134CrossRefGoogle Scholar
  27. Tanaka K, Sugeno M (1992) Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst 45:135–156MathSciNetCrossRefGoogle Scholar
  28. Tanaka K, Ikeda T, Wang HO (1998) Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans Fuzzy Syst 6(2):250–265CrossRefGoogle Scholar
  29. Wang L-X (1994) Adaptive fuzzy systems and control-design and stability analysis. Prentice-Hall, Englewood CliffsGoogle Scholar
  30. Wang L-X (1998) Universal approximation by hierarchical fuzzy systems. Fuzzy Sets Syst 93:223–230MathSciNetCrossRefGoogle Scholar
  31. Wang LX, Mendel JM (1992) Fuzzy basis functions, universal approximation, and orthogonal least-square learning. IEEE Trans Neural Netw 3:807–814CrossRefGoogle Scholar
  32. Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans Fuzzy Syst 4:14–23CrossRefGoogle Scholar
  33. Ying H (1994) Sufficient conditions on general fuzzy systems as function approximators. Automatica 30:521–C525CrossRefGoogle Scholar
  34. Ying H (1998a) General SISO Takagi–Sugeno fuzzy systems with linear rule consequent are universal approximators. IEEE Trans Fuzzy Syst 28:582–587CrossRefGoogle Scholar
  35. Ying H (1998b) Sufficient conditions on uniform approximation of multivariate functions by general Takagi–Sugeno fuzzy systems with linear rule consequent. IEEE Trans Syst Man Cybern 28:515–520CrossRefGoogle Scholar
  36. Zeng XJ, Singh MG (1994) Approximation theory of fuzzy systems - SISO case. IEEE Trans Fuzzy Syst 2:162–176CrossRefGoogle Scholar
  37. Zeng XJ, Singh MG (1995) Approximation theory of fuzzy systems - MIMO case. IEEE Trans Fuzzy Syst 3(2):219–235CrossRefGoogle Scholar
  38. Zhang YJ, Tao G, Chen M (2017) Parametrization and adaptive control of multivariable non-canonical T–S fuzzy systems. IEEE Trans Fuzzy Syst 25(1):156–171CrossRefGoogle Scholar
  39. Zhou SS, Feng G, Lam J, Xu SY (2005) Robust H-infinity control for discrete fuzzy systems via basis-dependent Lyapunov functions. Inf Sci 174(3–4):197–217CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ruiyun Qi
    • 1
  • Gang Tao
    • 2
  • Bin Jiang
    • 1
  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Engineering and Applied ScienceUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations