Skip to main content
Log in

An approach to design semi-global finite-time observers for a class of nonlinear systems

  • Special Focus
  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

In this paper, the problem of designing semi-global finite-time observers for a class of nonlinear systems is investigated. Based on the theories of finite-time stability, an approach to designing semi-global finite-time observers for the nonlinear systems is presented. It has been shown that, after the finite time, the designed finite-time observer realizes the accurate reconstruction of the states of the nonlinear system. A numerical example is given to illustrate the effectiveness and validity of the method.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cheng T, He X D, Asada H H. Nonlinear observer design for two phase flow heat exchangers of air conditioning systems. In: Proceedings of the 2004 American Control Conference (AAC). Boston: IEEE Press, 2004. 1534–1539

    Google Scholar 

  2. Kalman R E. On a new approach to filtering and prediction problems. Trans ASME J Basic Eng, 1960, 82(D): 35–45

    Google Scholar 

  3. Luenberger D G. An introduction to observers. IEEE Trans Autom Control, 1971, 16(6): 596–602

    Article  MathSciNet  Google Scholar 

  4. Zak S H. On the stabilization and observation of nonlinear uncertain dynamic systems. IEEE Trans Autom Control, 1990, 35(5): 604–607

    Article  MATH  MathSciNet  Google Scholar 

  5. Raghavan S. Observers and compensators for nonlinear system with application to flexible joint robot. PhD Thesis. Berkeley: Univ California, 1992

    Google Scholar 

  6. Engel R, Kreisselmeier G. A continuous-time observer which converges in finite time. IEEE Trans Autom Control, 2002, 47(7): 1202–1204

    Article  MathSciNet  Google Scholar 

  7. Menold P H, Findeisen R, Allgower F. Finite time convergent observers for linear time-varying systems. In: Proceedings of the 11th IEEE Mediterranem Conference on Control and Automation. Rhodos: IEEE Press, 2003

    Google Scholar 

  8. Menold P H, Findeisen R, Allgower F. Finite time convergent observers for nonlinear systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control. Maui: IEEE Press, 2003. 5673–5678

    Google Scholar 

  9. Ding Y Q, Liu Y G. An approach to design the finite time functional observer for a class of nonlinear systems (in Chinese). J Shandong Univ (Eng Sci), 2007, 37(1): 56–60

    MathSciNet  Google Scholar 

  10. Raff T, Menold P, Ebenbauer C, et al. A finite time functional observer for linear systems. In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville: IEEE Press, 2005. 7198–7203

    Chapter  Google Scholar 

  11. Bhat S P, Bernstein D S. Finite-time stability of continuous autonomous systems. SIAM J Contr Optim, 2000, 38(3): 751–766

    Article  MATH  MathSciNet  Google Scholar 

  12. Shen Y J, Xia X H. Semi-global finite-time observers for nonlinear systems. Automatica, 2008, 44(12): 3152–3156

    Article  MATH  MathSciNet  Google Scholar 

  13. Lei H, Lin W. Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach. Syst Control Lett, 2007, 56(7–8): 529–537

    Article  MATH  MathSciNet  Google Scholar 

  14. Bhat S P, Bernstein D S. Geometric homogeneity with applications to finite-time stability. Math Control Signals Syst, 2005, 17(2): 101–127

    Article  MATH  MathSciNet  Google Scholar 

  15. Qian C, Lin W. Non-lipschitz continuous stabilizer for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett, 2001, 42(3): 185–200

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to XiuCheng Deng.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 50779029), the Natural Science Foundation of Hubei Province (Grant No. 2008CDZ046), the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No. T200809) and the Science Foundation of Education Commission of Hubei Province (Grant No. D20091305)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deng, X., Shen, Y. An approach to design semi-global finite-time observers for a class of nonlinear systems. Sci. China Ser. F-Inf. Sci. 52, 1746–1753 (2009). https://doi.org/10.1007/s11432-009-0170-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-009-0170-1

Keywords