Skip to main content
SpringerLink
Log in

On global stabilization of a class of nonlinear systems with high-order nonlinearities by state feedback

  • Technical Notes and Correspondence
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

We consider a problem of global stabilization of a class of nonlinear systems. The considered nonlinear systems are in the approximately feedback linearized form and perturbed nonlinear terms contain high-order terms. We propose a control law that has a dynamic controller gain which is effectively tuned to deal with high-order nonlinear terms. Our new method broadens a class of nonlinear systems under consideration over the existing results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Barbu, R. Sepulchre, W. Lin, and P. V. Kokotović, “Global asymptotic stabilization of the ball-and-beam system,” Proc. of the 36th Conf. on Decision and Control, pp. 2351–2355, 1997.

  2. H.-L. Choi and J.-T. Lim, “On robust approximate feedback linearization,” IEICE Trans. Fundamentals, vol. E87-A, no. 2, 502–504, 2004.

    Google Scholar 

  3. H.-L. Choi and J.-T. Lim, “Global exponential stabilization of a class of nonlinear systems by output feedback,” IEEE Trans. Automat. Contr., vol. 50, no. 2, pp. 255–257, 2005.

    Article  MathSciNet  Google Scholar 

  4. H.-L. Choi and J.-T. Lim, “Stabilization of a class of nonlinear systems by adaptive output feedback,” Automatica, vol. 41, no. 6, pp. 1091–1097, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. A. Freeman and P. V. Kokotović, “Design of ’softer’ robust nonlinear control laws,” Automatica, vol. 29, no. 6, pp. 1425–1437, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Hauser, S. Sastry, and P. Kokotović, “Nonlinear control via approximate input-output linearization: the ball and beam example,” IEEE Trans. on Automat. Contr., vol. 37, no. 3, 392–398, 1992.

    Article  Google Scholar 

  7. H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ 07458, 2002.

    MATH  Google Scholar 

  8. P. Krishnamurthy and F. Khorrami, “High-gain scaling technique for adaptive output feedback control of feedforward systems,” IEEE Trans. Automat. Contr., vol. 49, no. 12, pp. 2286–2292, 2004.

    Article  MathSciNet  Google Scholar 

  9. M. Krstić, I. Kanellakopoulos, and P. Kokotović, Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, 2005.

    Google Scholar 

  10. H. Lei and W. Lin, “Universal adaptive control of nonlinear systems with unknown growth rate by output feedback,” Automatica, vol. 42, no. 10, pp. 1783–1789, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. Lei and W. Lin, “Robust control of uncertain nonlinear systems by output feedback,” Proc. of the American Control Conf., July, pp. 5354–5359, 2007.

  12. R. Olfari-Saber, “Fixed point controllers and stabilization of the cart-pole system and the rotating pendulum,” Proc. of the 38th Conf. on Decision and Control, pp. 1174–1181, 1999.

  13. C. Qian and W. Lin, “Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm,” IEEE Trans. on Automat. Contr., vol. 47, no. 10, pp. 1710–1715, 2002.

    Article  MathSciNet  Google Scholar 

  14. Y. Xudong, “Universal stabilization of feedforward nonlinear systems,” Automatica, vol. 39, no. 1, pp. 141–147, 2003.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong Yuseong-gu, Daejeon, 305-701, Korea

    Min-Sung Koo & Jong-Tae Lim

  2. Dept. of Electrical Engineering, Dong-A University, Hadan2-dong, Saha-gu, Busan, 604-714, Korea

    Ho-Lim Choi

Authors
  1. Min-Sung Koo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ho-Lim Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jong-Tae Lim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ho-Lim Choi.

Additional information

Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il Lee. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0063942).

Min-Sung Koo received her B.S. and M.S. degrees in Electrical Engineering from Korea Advanced Institute of Science and Technology in 2004 and 2006, respectively, where she is currently working toward a Ph.D. degree. Her research interests include nonlinear control, adaptive control, and switching systems.

Ho-Lim Choi received his B.S.E. degree in Electrical Engineering from The Univ. of Iowa in 1996, and his M.S. and Ph.D. degrees in 1999 and 2004 from KAIST. Currently, he is an assistant professor at the department of Electrical Engineering, Dong-A University. His research interests include nonlinear control, adaptive control, output feedback control, and time-delay systems.

Jong-Tae Lim received his B.S.E.E. degree in Electrical Engineering from Yonsei University in 1975 and an M.S.E.E degree from the Illinois Institute of Technology, Chicago, in 1983, and a Ph.D. degree in Computer, Information and Control Engineering from the University of Michigan, Ann Arbor, in 1986. He is currently a professor in the Division of Electrical Engineering at the Department of EECS, KAIST. His research interests are in the areas of systems and control theory, communication network, and discrete event systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koo, MS., Choi, HL. & Lim, JT. On global stabilization of a class of nonlinear systems with high-order nonlinearities by state feedback. Int. J. Control Autom. Syst. 8, 908–912 (2010). https://doi.org/10.1007/s12555-010-0426-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-010-0426-y

Keywords

Search

Navigation