Skip to main content
SpringerLink
Log in
Book cover

International Conference on Fuzzy Systems and Knowledge Discovery

FSKD 2005: Fuzzy Systems and Knowledge Discovery pp 930–941Cite as

Relaxed LMIs Observer-Based Controller Design via Improved T-S Fuzzy Model Structure

  • Conference paper

  • 1472 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3613))

Abstract

Relaxed linear matrix inequalities (LMIs) conditions for fuzzy observer-based controller design are proposed based on a kind of improved T-S fuzzy model structure. The improved structure included the original T-S fuzzy model and enough large bandwidth pre- and post-filters. By this structure fuzzy observer-based controller design can be transformed into LMIs optimization problem. Compared with earlier results, it includes the less number of LMIs that equals the number of fuzzy rules plus one positive definition constraint of Lyapunov function. Therefore, it provides us with less conservative results for fuzzy observer-based controller design. Finally, a numerical example is demonstrated to show the efficiency of proposed method.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear matrix inequalities in systems and control theory. SIAM, Philadelphia (1994)

    Google Scholar 

  2. Castro, J.: Fuzzy logic controllers are universal approximator. IEEE Trans. on Systems, Man, Cybernetics 25, 629–635 (1995)

    Article  Google Scholar 

  3. Chadli, M., Maquin, D., Ragot, J.: Relaxed stability conditions for Takagi-Sugeno fuzzy systems. In: IEEE International Conference on Systems, Man, and Cybernetics, Nashville, Tennessee, USA, October 8-11, pp. 3514–3519 (2000)

    Google Scholar 

  4. Chai, J.-S., Tan, S., Chan, Q., Hang, C.-C.: A general fuzzy control scheme for nonlinear processes with stability analysis. Fuzzy Sets and Systems 100, 179–195 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gahinet, P., Nemirovskii, A., Laub, A.J., Chilali, M.: LMI toolbox. Mathworks, Natick (1995)

    Google Scholar 

  6. Jadbabaie, A.: A reduction in conservatism in stability and L2 Gain analysis of T-S fuzzy systems via Linear matrix inequalities. In: IFAC 1999. triennial World congress, vol. 14, pp. 285–289. P.R. China (1999)

    Google Scholar 

  7. Johansson, M., Rantzer, A., Arz6n, K.: Piecewise quadratic stability for affine Sugeno systems. In: FUZZ. IEEE 1998, Anchorage, Alaska (1998)

    Google Scholar 

  8. Jadbabaie, A.: A reduction in conservatism in stability and L2 Gain analysis of T-S fuzzy systems via Linear matrix inequalities. In: IFAC 1999. triennial World congress, vol. 14, pp. 285–289. P.R. China, Beijing (1999)

    Google Scholar 

  9. Liu, X.D., Zhang, Q.L.: New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica 39, 1571–1582 (2003)

    Article  MATH  Google Scholar 

  10. Narendra, K.S., Balakrishnan, J.: A common Lyapunov function for stable LTI systems with commuting A-matrices. IEEE Trans. on Automatic Control 39(12), 2469–2471 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  11. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. on Systems, Man, Cybernetics 15(l), 116–132 (1985)

    MATH  Google Scholar 

  12. Takagi, T., Ikeda, T., Wang, H.O.: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based design. IEEE Trans. on Fuzzy Systems 6(2), 250–256 (1998)

    Article  Google Scholar 

  13. Tanaka, K., Ikeda, T., Wang, H.O.: Robust stabilization of uncertain non-linear systems via fuzzy control: quadratic stability, H control theory, and LMIs. IEEE Trans. on Fuzzy Systems 4(1), 1–12 (1996)

    Article  Google Scholar 

  14. Tanaka, K., Sugeno, M.: Stability and design of fuzzy control systems. Fuzzy Set and Systems 45(2), 135–156 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tanaka, K., Nishimuna, M., Wang, H.O.: Multi-objective fuzzy control of high rise/high speed elevators using LMIs. In: American Control Conference, Philadelphia, Pennsylvanie, June 1998, pp. 3450–3454 (1998)

    Google Scholar 

  16. Teixeira, M.C.M., Zak, S.H.: Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE. Trans. on Fuzzy Systems 7(2), 133–140 (1999)

    Article  Google Scholar 

  17. Thierry, M.G., Laurent, V.: Control laws for Takagi-Sugeno fuzzy models. Fuzzy Sets and Systems 120, 95–108 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Wang, H.O., Tanaka, K., Griffin, M.F.: An approach to fuzzy control of nonlinear systems: stability and design: issues. IEEE. Trans. on Fuzzy Systems 4(l) (1996)

    Google Scholar 

  19. Bupp, R.T., Bernstein, D.S., Coppola, V.T.: A benchmark problem for nonlinear control design: problem statement, experimental testbed, and passive nonlinear compensation. In: Proceedings of American Control Conference, Seattle, WA, USA, June 21-23, vol. 6, pp. 4363–4367 (1995)

    Google Scholar 

  20. Wang, L.-X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Satellite Venture Business Laboratory, Kitami Institute of Technology, 165 Koencho, Kitami, Hokkaido, 090-8507, Japan

    Wei Xie

  2. College of Information Science and Technology, Wuhan University of Science and Technology, Wuhan, 430081, Hubei Province, P. R. China

    Huaiyu Wu & Xin Zhao

Authors
  1. Wei Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaiyu Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, Nanyang Avenue, 639798, Singapore

    Lipo Wang

  2. Honda Research Institute Europe GmbH, Offenbach/Main, Germany

    Yaochu Jin

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xie, W., Wu, H., Zhao, X. (2005). Relaxed LMIs Observer-Based Controller Design via Improved T-S Fuzzy Model Structure. In: Wang, L., Jin, Y. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2005. Lecture Notes in Computer Science(), vol 3613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539506_116

Download citation

  • DOI: https://doi.org/10.1007/11539506_116

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28312-6

  • Online ISBN: 978-3-540-31830-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation