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

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 297))

Abstract

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.

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References

  1. Sontag, E.D.: Nonlinear regulation: the piecewise linear approach. IEEE Trans. Autom. Control 26, 346–357 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Johansson, M., Rantzer, A.: Computation of piecewise quadratic lyapunov functions of hybrid systems. IEEE Trans. Autom. Control 43, 555–559 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Imura, J., van der Schaft, A.: Characterization of well-posedness of piecewise-linear systems. IEEE Trans. Autom. Control 45, 1600–1619 (2000)

    Article  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  5. Sugeno, M.: On stability of fuzzy systems expressed by fuzzy rules with singleton consequents. IEEE Trans. Fuzzy Syst. 7, 201–224 (1999)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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. 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. 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. Guarabassi, G.O., Savaresi, S.M.: Approximate linearization via feedback - an overview. Automatica 37, 1–15 (2001)

    Article  Google Scholar 

  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. Khalil, H.K.: In: Nonlinear systems, 3rd edn. Prentice hall (2002)

    Google Scholar 

  14. Isidori, A.: The matching of a prescribed linear input-output behavior in a nonlinear system. IEEE Trans. Autom. Control 30, 258–265 (1985)

    Article  MathSciNet  MATH  Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Taniguchi, T., Sugeno, M. (2012). Robust Stabilization of Nonlinear Systems Modeled with Piecewise Bilinear Systems Based on Feedback Linearization. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances on Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31709-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-31709-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31708-8

  • Online ISBN: 978-3-642-31709-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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