Nonlinear Dynamics

, Volume 79, Issue 1, pp 359–368 | Cite as

On observer for a class of uncertain nonlinear systems

  • T. Khalifa
  • M. Mabrouk
Original Paper


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.


Uncertain nonlinear systems Unknown parameters Observers Practical observers 


  1. 1.
    Andrieu, V., Praly, L., Astolfi, A.: High gain observers with updated gain and homogeneous correction terms. Automatica 45, 422–428 (2009)CrossRefMATHMathSciNetGoogle Scholar
  2. 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)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Benabdallah, A., Kharrat, T., Vivalda, J.-C.: On practical observers for nonlinear uncertain systems. Syst. Control Lett. 57, 371–377 (2008)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Bullinger, E., Allgöwer, F.: An adaptive high-gain observer for nonlinear systems. In: CDC (2007)Google Scholar
  5. 5.
    Farza, M., M’Saad, M., Maatoog, T.: High gain observer for a class of non-triangular systems, Syst. Control Lett. (2011)Google Scholar
  6. 6.
    Gauthier, J.P., Hammouri, H., Othman, S.: A simple observer for nonlinear systems. IEEE Trans. Autom. Control 37, 875–880 (1992)Google Scholar
  7. 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)Google Scholar
  8. 8.
    Ilchmann, A.: Non-identifier-based high gain adaptive control. In: Lecture Notes in Control and Information Sciences, vol. 189. Springer, Berlin (1993)Google Scholar
  9. 9.
    Krener, A., Isidori, A.: Linearization by output injection and nonlinear observers. Syst. Control Lett. 3(1), 47–52 (1983)CrossRefMATHMathSciNetGoogle Scholar
  10. 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)Google Scholar
  11. 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)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Praly, L., Jiang, Z.P.: Linear output feedback with dynamic high gain for nonlinear systems. Syst. Control Lett. 53, 107–116 (2004) Google Scholar
  13. 13.
    Rapaport, A., Gouze, J.L.: Parallelotopic and practical observers for nonlinear uncertain systems. Int. J. Control 76(3), 237–251 (2003)CrossRefMATHMathSciNetGoogle Scholar
  14. 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)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Tornambè, A.: High-gain observers for nonlinear systems. Int. J. Syst. Sci. 23(9), 1475–1489 (1992)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.ESST, Hammam SousseSousseTunisia
  2. 2.Department of MathematicsCollege of Applied SciencesMeccaKSA
  3. 3.Department of Mathematics, Faculty of Sciences of GabèsUniversity of GabèsGabèsTunisia

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