Robust Stabilization of Nonlinear Systems Modeled with Piecewise Bilinear Systems Based on Feedback Linearization

  • Tadanari Taniguchi
  • Michio Sugeno
Part of the Communications in Computer and Information Science book series (CCIS, volume 297)


This paper deals with the robust stabilization of nonlinear control systems by approximating with piecewise bilinear models. The approximated systems are thus found to be piecewise bilinear. The input-output feedback linearization is applied to design the controllers for piecewise bilinear systems. This paper suggests a method to design robust stabilizing controllers, considering modeling errors. Illustrative example is given to show the validity of the proposed method.


Nonlinear System Robust Stabilization Feedback Linearization Nonlinear Control System Piecewise Linear Approximation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sontag, E.D.: Nonlinear regulation: the piecewise linear approach. IEEE Trans. Autom. Control 26, 346–357 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Johansson, M., Rantzer, A.: Computation of piecewise quadratic lyapunov functions of hybrid systems. IEEE Trans. Autom. Control 43, 555–559 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Imura, J., van der Schaft, A.: Characterization of well-posedness of piecewise-linear systems. IEEE Trans. Autom. Control 45, 1600–1619 (2000)zbMATHCrossRefGoogle Scholar
  4. 4.
    Feng, G., Lu, G.P., Zhou, S.S.: An approach to hinfinity controller synthesis of piecewise linear systems. Communications in Information and Systems 2, 245–254 (2002)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Sugeno, M.: On stability of fuzzy systems expressed by fuzzy rules with singleton consequents. IEEE Trans. Fuzzy Syst. 7, 201–224 (1999)CrossRefGoogle Scholar
  6. 6.
    Sugeno, M., Taniguchi, T.: On improvement of stability conditions for continuous mamdani-like fuzzy systems. IEEE Tran. Systems, Man, and Cybernetics, Part B 34, 120–131 (2004)CrossRefGoogle Scholar
  7. 7.
    Taniguchi, T., Sugeno, M.: Stabilization of nonlinear systems based on piecewise lyapunov functions. In: FUZZ-IEEE 2004, pp. 1607–1612 (2004)Google Scholar
  8. 8.
    Goh, K.-C., Safonov, M.G., Papavassilopoulos, G.P.: A global optimization approach for the BMI problem. In: Proc. the 33rd IEEE CDC, vol. 3, pp. 2009–2014 (1994)Google Scholar
  9. 9.
    Taniguchi, T., Sugeno, M.: Piecewise bilinear system control based on full-state feedback linearization. In: SCIS & ISIS 2010, pp. 1591–1596 (2010)Google Scholar
  10. 10.
    Taniguchi, T., Sugeno, M.: Stabilization of nonlinear systems with piecewise bilinear models derived from fuzzy if-then rules with singletons. In: FUZZ-IEEE 2010, pp. 2926–2931 (2010)Google Scholar
  11. 11.
    Guarabassi, G.O., Savaresi, S.M.: Approximate linearization via feedback - an overview. Automatica 37, 1–15 (2001)CrossRefGoogle Scholar
  12. 12.
    Taniguchi, T., Sugeno, M.: Design of LUT-controllers for nonlinear systems with PB models based on I/O linearization. In: FUZZ-IEEE (to appear, 2012)Google Scholar
  13. 13.
    Khalil, H.K.: In: Nonlinear systems, 3rd edn. Prentice hall (2002)Google Scholar
  14. 14.
    Isidori, A.: The matching of a prescribed linear input-output behavior in a nonlinear system. IEEE Trans. Autom. Control 30, 258–265 (1985)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tadanari Taniguchi
    • 1
  • Michio Sugeno
    • 2
  1. 1.Tokai UniversityHiratsukaJapan
  2. 2.European Centre for Soft ComputingMieresSpain

Personalised recommendations