Advertisement

Static Output Feedback Control for Fuzzy Systems

  • Abdellah BenzaouiaEmail author
  • Ahmed El Hajjaji
Chapter
  • 1k Downloads
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 8)

Abstract

This chapter presents a static output feedback controller design method for nonlinear systems represented by Takagi-Sugeno (T–S) fuzzy models. A new quadratic stabilization result based on Parallel Distributed Compensation (PDC) structure is developed to design a static output PDC (OPDC) controller. Based on the well known existing method in the literature, two methods are proposed. The design of the controller by static output feedback is given by two different sets of LMIs. Two examples are presented to illustrate these results.

Keywords

Lyapunov Function Fuzzy System Static Output Feedback Quadratic Lyapunov Function Common Lyapunov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Elghaoui L, Oustry F, Aitrami M (1997) A cone complementary linearization algorithm for static output-feedback and related problems. IEEE Trans Aut Control 42:1171–1176CrossRefMathSciNetGoogle Scholar
  2. 2.
    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, 10–13 Dec 2002, pp 311–316Google Scholar
  3. 3.
    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
  4. 4.
    Daafouz J, Riedinger P, Iung C (2002) Stability analysis and control synthesis for switched systems: a switched Lyapunov function spproach. IEEE Trans Aut Control 47:1883–11887CrossRefMathSciNetGoogle Scholar
  5. 5.
    Feng G (2004) Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans Fuzzy Syst 12:22–28CrossRefGoogle Scholar
  6. 6.
    Johansson M, Rantzer A, Arzen KE (1999) Piecewise quadratic stability of fuzzy systems. IEEE Trans Fuzzy Syst 7:713–722CrossRefGoogle Scholar
  7. 7.
    Shorten R, Narenda KS, Mason O (2003) A result on common quadratic Lyapunov functions. IEEE Trans Aut Control 48:110–113CrossRefGoogle Scholar
  8. 8.
    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, Greece, 2–5 July 2007Google Scholar
  9. 9.
    Nachidi M, Tadeo F, Hmamed A, Benzaouia A (2007) Static output-feedback stabilization for time-delay Takagi-Sugeno fuzzy systems. In: \(46^{th}\) Conference decision control. New Orleans, 12–14 Dec 2007, pp 1634–1639Google Scholar
  10. 10.
    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 16:1188–1196Google Scholar
  11. 11.
    De Olivera MC, Skelton RE (2001) Stability tests for constrained linear systems, perspective in robust control. Springer, LNCISGoogle Scholar
  12. 12.
    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 2:119–134CrossRefGoogle Scholar
  13. 13.
    Yoneyama Y, Nishikawa M, Katayama H, Ichikawa A (2000) Output stabilization of Takagi-Sgugeno fuzzy systems. Fuzzy Sets Syst 111:253–266CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Benzaouia A (2012) Saturated switching systems. Springer, SLNCCrossRefGoogle Scholar
  15. 15.
    Nachidi M (2009) Stabilization of Takagi-Sugeno fuzzy systems with application on a greenhouse (Ph. D. thesis). University of Valladolid, SpainGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of Cadi AyyadMarrakechMorocco
  2. 2.Laboratoire de Modélisation, Information et SystèmesUniversité de Picardie Jules VerneAmiensFrance

Personalised recommendations