Skip to main content
SpringerLink
Log in

On observer for a class of uncertain nonlinear systems

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper considers the problem of estimating the unmeasurable states for a family of uncertain nonlinear systems. For systems with bounded trajectories, we propose a weak practical observer (see Definition 1). When the trajectories are unbounded, under the assumption that the nonlinearity is bounded, we construct a global time-varying observer. Finally, an example is provided to verify the effectiveness of the observer.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Andrieu, V., Praly, L., Astolfi, A.: High gain observers with updated gain and homogeneous correction terms. Automatica 45, 422–428 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ben Hamed, B., Haj Salem, Z., Hammami, M.-A.: Stability of nonlinear time-varying perturbed differential equations. Nonlinear Dyn. 73(3), 1353–1365 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Benabdallah, A., Kharrat, T., Vivalda, J.-C.: On practical observers for nonlinear uncertain systems. Syst. Control Lett. 57, 371–377 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bullinger, E., Allgöwer, F.: An adaptive high-gain observer for nonlinear systems. In: CDC (2007)

  5. Farza, M., M’Saad, M., Maatoog, T.: High gain observer for a class of non-triangular systems, Syst. Control Lett. (2011)

  6. Gauthier, J.P., Hammouri, H., Othman, S.: A simple observer for nonlinear systems. IEEE Trans. Autom. Control 37, 875–880 (1992)

  7. Guo, B.-Z., Zhao, Z.-L.: On the convergence of an extended state observer for nonlinear systems with uncertainty. Syst. Control Lett. 60(6), 420–430 (2011)

  8. Ilchmann, A.: Non-identifier-based high gain adaptive control. In: Lecture Notes in Control and Information Sciences, vol. 189. Springer, Berlin (1993)

  9. Krener, A., Isidori, A.: Linearization by output injection and nonlinear observers. Syst. Control Lett. 3(1), 47–52 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lei, H., Wei, J., Lin, W.: A global observer for observable autonomous systems with bounded solution trajectories. In: Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain, pp. 1911–1916 (2005)

  11. Lei, H., Wei, J., Lin, W.: A global observer for autonomous systems with bounded trajectories. Int. J. Robust Nonlinear Control 17, 1088–1105 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Praly, L., Jiang, Z.P.: Linear output feedback with dynamic high gain for nonlinear systems. Syst. Control Lett. 53, 107–116 (2004)

  13. Rapaport, A., Gouze, J.L.: Parallelotopic and practical observers for nonlinear uncertain systems. Int. J. Control 76(3), 237–251 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  14. Tian, W., Dua, H., Qian, C.: A semi-global finite-time convergent observer for a class of nonlinear systems with bounded trajectories. Nonlinear Anal. Real World Appl. 13, 1827–1836 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tornambè, A.: High-gain observers for nonlinear systems. Int. J. Syst. Sci. 23(9), 1475–1489 (1992)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ESST, Hammam Sousse, Rue Lamine Abessi, 4011, Sousse, Tunisia

    T. Khalifa

  2. Department of Mathematics, College of Applied Sciences, P. O. Box 715, Mecca, 21955, KSA

    M. Mabrouk

  3. Department of Mathematics, Faculty of Sciences of Gabès, University of Gabès, Cité Erriadh, Zrig, 6072, Gabès, Tunisia

    M. Mabrouk

Authors
  1. T. Khalifa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Mabrouk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Mabrouk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khalifa, T., Mabrouk, M. On observer for a class of uncertain nonlinear systems. Nonlinear Dyn 79, 359–368 (2015). https://doi.org/10.1007/s11071-014-1669-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1669-6

Keywords

Search

Navigation