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Introduction to Takagi–Sugeno Fuzzy Systems

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Advanced Takagi‒Sugeno Fuzzy Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 8))

Abstract

The T–S fuzzy approach has known a great interest of researchers many years ago [1–5]. The idea of this approach is to describe the comportment of a nonlinear system by a finite number of local linear subsystems inside different operating regions.

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References

  1. Huang D, Nguang SK (2007) Static output feedback controller design for fuzzy systems: an LMI approach. Inf Sci 177:3005–3015

    Article  MATH  MathSciNet  Google Scholar 

  2. Huai-Ning W (2008) An ILMI approach to robust \(H_2\) static output feedback fuzzy control for uncertain discrete-time nonlinear systems. Automatica 44:2333–2339

    Article  MATH  Google Scholar 

  3. Kau S, Lee H, Yang CM, Lee CH, Hong L, Fang CH (2007) Robust \(H_{\infty }\) fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties. Fuzzy Sets Syst 158: 135–146

    Google Scholar 

  4. Lo JC, Lin ML (2003) Robust H\(_\infty \) nonlinear control via fuzzy static output feedback. IEEE Trans Circuits Syst I(50):1494–1502

    Google Scholar 

  5. Wang LX, Mendel JM (1992) Fuzzy basis functions, universal approximation and orthogonal least-squares. IEEE Trans Neural Netw 3:807–814

    Article  Google Scholar 

  6. Babuska R (1998) Fuzzy modeling for control. Kluwer Acadimec Publishers, Boston

    Book  Google Scholar 

  7. Gasso K (2000) Identification des Systèmes Dynamiques non Linéaires: Approche Multimodèles. PhD thesis of Lorraine University, France

    Google Scholar 

  8. Wu HC, Lu CN (1999) Automatic fuzzy model identification for short term load forecast. IEEE Gener Transm Distrib 146:477–482

    Article  Google Scholar 

  9. El Hajjaji A, Chadli M, Oudghiri M, Pages O (2006) Observer-based robust fuzzy control for vehicle lateral dynamics. In: IEEE American Control Conference, Minneapolis, pp 4664–4669, 14–16 June 2006

    Google Scholar 

  10. Guerra TM, Vermeirn L (2001) Control laws for Takagi-Sugeno fuzzy models. Fuzzy Sets Syst 33:95–108

    Article  Google Scholar 

  11. Tanaka K, Wang HO (2001) Fuzzy control systems design and analysis: a linear matrix inequality approach. Wiley, New York

    Book  Google Scholar 

  12. Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design Issues. IEEE Trans Fuzzy Syst 4:14–23

    Article  Google Scholar 

  13. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15:116–132

    Article  MATH  Google Scholar 

  14. Buckley JJ (1992) Universal fuzzy controllers. Automatica 28:1245–1248

    Article  MATH  MathSciNet  Google Scholar 

  15. Castro J (1995) Fuzzy logic controllers are universal approximator. IEEE Trans Syst Man Cybern-C 25:629–635

    Article  Google Scholar 

  16. Gasso K, Mourot G, Ragot J (2002) Structure identification of multiple models with output error local models. In: Proceeding of the 15th World Congress IFAC, Barcelona 22–26 July 2002

    Google Scholar 

  17. Teixeira MCM, Stanislaw H (1999) Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE Trans Fuzzy Syst 7:133–142

    Article  Google Scholar 

  18. Tanaka K, Ikeda T, Wang HO (1996) Robust Stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \(H_{\infty }\) control theory and linear matrix inequalities. IEEE Trans Fuzzy Syst 4:1–13

    Article  Google Scholar 

  19. El Hajjaji A, Chadli M (2009) Commande Basée sur la Modélisation Floue de Type Takagi-Sugeno d’un Procédé Expérimental á Quatres Cuves. e-STA 6:46–51

    Google Scholar 

  20. Kim E, Lee H (2000) New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Trans Fuzzy Syst 8:523–534

    Google Scholar 

  21. Liu X, Qingling Z (2003) New approaches to \(H_{\infty }\) controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica 39:1571–1582

    Article  MATH  Google Scholar 

  22. Hindi H, Boyd S (1998) Analysis of Linear systems with saturating using convex optimization. In: Proceeding of 37th IEEE conference decision control, Florida-Tampa, pp 903–908, 16–18 Dec 1998

    Google Scholar 

  23. Johansson M, Rantzer A, Arzen K (1998) Piecewise quadratic stability for affine Sugeno systems. IEEE Int Conf Fuzzy Syst 1:55–60

    Google Scholar 

  24. Benzaouia A, Mehdi D, El Hajjaji A, Nachidi M (2007) Piecewise quadratic Lyapunov function for nonlinear systems with fuzzy static output feedback control. In: European control conference, Kos 2–5 July 2007

    Google Scholar 

  25. Guerra TM, Vermeiren L (2004) LMI-based relaxed non quadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno’s form. Automatica 40:823–829

    Article  MATH  MathSciNet  Google Scholar 

  26. Chadli M, Maquin D, Ragot J (2002) An LMI formulation for output feedback stabilization in multiple model approach. In: 41th conference decision control, Las Vegas, pp 311–316, 10–13 Dec 2002

    Google Scholar 

  27. Tuan HD, Apkarian P, Narikiyo T, Yamamoto Y (2001) Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Trans Fuzzy Syst 9:324–332

    Article  Google Scholar 

  28. Cao YY, Lam J, Sun YX (1998) Static output feedback stabilization: an LMI Approach. Automatica 34:1641–1645

    Google Scholar 

  29. Cao YY, Lam J, Sun YX (1998) Analysis and design for a class of complex control systems partII: Fuzzy controller Design. Automatica 33:1029–1039

    Google Scholar 

  30. Kar IN (1999) Design of static output feedback controller for uncertain systems. Automatica 35:169–175

    Article  MATH  MathSciNet  Google Scholar 

  31. Nachidi M, Benzaouia A, Tadeo F, Ait Rami M (2008) LMI-based approach for output feedback stabilization for discrete-time Takagi-Sugeno systems. IEEE Trans Fuzzy Syst 16:1188–1196

    Google Scholar 

  32. Chadli M, Maquin D, Ragot J (2002) Static Output feedback for Takagi-Sugeno systems: an LMI approach. In: Medical Conference of Control and Automation, Lisbon 9–13 July 2002

    Google Scholar 

  33. Chadli M, El hajjaji A (2005) Output Robust stabilization of uncertain Takagi-Sugeno model. In: 44th IEEE conference of decision control-European control Conference, Sevilla, pp 3393–3398, 12–15 Dec 2005

    Google Scholar 

  34. Chadli M, El Hajjaji A (2006) A observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets Syst 157:1276–1281

    Article  MATH  Google Scholar 

  35. Patton RJ, Chen J, Lopez-Toribio C (1998) Fuzzy observer for nonlinear dynamic systems fault diagnosis. In: IEEE Conference of decision control, Tampa, pp 84–89, 16–18 Dec 1998

    Google Scholar 

  36. Shaocheng T, Yiqian T (2000) Analysis and design of fuzzy robust observer for uncertain nonlinear systems. In: IEEE international conference fuzzy systems, vol 2, pp 993–996, May 7–10 2000

    Google Scholar 

  37. Ma XZ, Sun ZQ, He YY (1998) Analysis and design of fuzzy controller and fuzzy observer. IEEE Trans Fuzzy Syst 6:41–51

    Google Scholar 

  38. Daraoui N, Pages O, EL Hajjaji A (2012) Robust Role and yaw control systems using fuzzy models of the vehicle dynamics. In: IEEE international conference of fuzzy systems (FUZZ-IEEE), Brisban, pp 1–6, 10–15 June 2012

    Google Scholar 

  39. Ghorbel H, El Hajjaji A, Souissi M, Chaabane M (2013) Improvement on observer-based \(H\infty \) tracking control for TS fuzzy systems with unmeasurable premise variables. In: 52nd IEEE conference on decision and control, Florence 10–13 Dec 2013

    Google Scholar 

  40. Ichalal D, Marx B, Ragot J, Maquin D (2012) Advances in observer design for Takagi–Sugeno systems with unmeasurable premise variables. In: 20th IEEE mediterranean conference control automation, Barcelona, pp 848–853, 3–6 July 2012

    Google Scholar 

  41. Lee KR, Jeung ET, Park HB (2001) Robust fuzzy \(H_{\infty }\) control for uncertain nonlinear systems via state feedback: an LMI approach. Fuzzy Sets Syst 120:123–134

    Article  MATH  MathSciNet  Google Scholar 

  42. Oudghiri M, Chadli M, El Hajjaji A (2007) One-step procedure for robust output fuzzy control. In: 15th IEEE mediterranean conference of control automation, Athens, pp 1–6, 27–29 June 2007

    Google Scholar 

  43. El Messoussi W, Pages O, El Hajjaji A (2006) Observer-based robust control of uncertain fuzzy dynamic systems with pole placement constraints: an LMI approach. In: American control conference, Minneapolis, pp 2203–2208, 14–16 June 2006

    Google Scholar 

  44. Shaocheng T, Han-Hiong L (2002) Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets Syst 131:165–184

    Article  MATH  Google Scholar 

  45. Lin C, Wang Q, Lee T (2005) Improvement on observer-based \(H_{\infty }\) control for T-S fuzzy systems. Automatica 41:1651–1656

    Article  MATH  MathSciNet  Google Scholar 

  46. Xiaodong L, Gingling Z (2003) New approaches to \(H_{\infty }\) controller design based on fuzzy observers for T-S fuzzy systems via LMI. Automatica 39:1571–1582

    Article  MATH  Google Scholar 

  47. Lo J, Lin M (2004) Robust \(H\infty \) nonlinear modeling and control via uncertain fuzzy systems. Fuzzy Sets Syst 143:189–209

    Article  MATH  MathSciNet  Google Scholar 

  48. Gopalsamy K (1992) Stability and oscillations in delay differential equations of population dynamics. Kluwer Academic Publishers, New York

    Google Scholar 

  49. Kolmanovskii VB, Myshkis AD (1992) Applied theory of functional differential equations. Kluwer Academic Publishers, New York

    Google Scholar 

  50. Kolmanovskii VB, Myshkis AD (1999) Introduction to the theory and applications of functional differential equations. Kluwer Academic Publishers, New York

    Google Scholar 

  51. Cao SG, Rees W, Feng G (2001) \(H_{\infty }\) control of uncertain dynamical fuzzy discrete-time systems. IEEE Trans Syst Man Cybern-B 31:802–812

    Article  Google Scholar 

  52. Chen B, Liu X (2005) Delay-dependent robust \(H_{\infty }\) control for T-S fuzzy systems with time delay. IEEE Trans Fuzzy Syst 13:238–249

    Article  Google Scholar 

  53. Guan XP, Chen CL (2004) Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays. IEEE Trans Fuzzy Syst 12:236–249

    Article  MATH  Google Scholar 

  54. Li C, Wang H, Liao X (2004) Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays. Proc Inst Elect Eng Control Theor Appl 151:417–421

    Article  Google Scholar 

  55. Wu HN, Li HX (2007) New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay. IEEE Trans Fuzzy Syst 15:482–493

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Cadi Ayyad, Marrakech, Morocco

    Abdellah Benzaouia

  2. Laboratoire de Modélisation, Information et Systèmes, Université de Picardie Jules Verne, Amiens, France

    Ahmed El Hajjaji

Authors
  1. Abdellah Benzaouia
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  2. Ahmed El Hajjaji
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Correspondence to Abdellah Benzaouia .

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Benzaouia, A., El Hajjaji, A. (2014). Introduction to Takagi–Sugeno Fuzzy Systems. In: Advanced Takagi‒Sugeno Fuzzy Systems. Studies in Systems, Decision and Control, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05639-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-05639-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05638-8

  • Online ISBN: 978-3-319-05639-5

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