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Observers with Discrete-Time Measurements in the Sliding Mode Output-Feedback Stabilization of Nonlinear Systems

  • Elisabetta Punta
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 440)

Abstract

The chapter investigates the problem of designing an observer for nonlinear nonaffine systems with discrete-time measurements (continuous-discrete-time systems). The chapter considers the variable-structure control of nonlinear systems when the state vector is not completely available and the output measurements are discrete-time; the use of suitably designed observers is required. The strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems. An observer is proposed and conditions are found under which the convergence to the unique ideal solution is proven for both system and observer. The control problem is solved by forcing a sliding regime for the observer, while satisfying an exponential stability criterion for the observation error state equation.

Keywords

Slide Mode Control Output Feedback Input Channel Mode Observer Nonlinear Observer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bartolini, G., Zolezzi, T.: Dynamic output feedback for observed variable-structure control systems. Systems & Control Letters 7(3), 189–193 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bartolini, G., Zolezzi, T.: Control of nonlinear variable structure systems. J. Math. Anal. Appl. 118, 42–62 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bartolini, G., Punta, E.: Reduced-order observer in the sliding-mode control of nonlinear nonaffine systems. IEEE Trans. Automatic Control 55(10), 2368–2373 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bartolini, G., Ferrara, A., Usai, E.: Chattering avoidance by second order sliding modes control. IEEE Trans. Automatic Control 43(2), 241–247 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bartolini, G., Ferrara, A., Usai, E., Utkin, V.I.: On multi-input chattering-free second order sliding mode control. IEEE Trans. Automatic Control 45(9), 1711–1717 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Boiko, I., Fridman, L., Pisano, A., Usai, E.: Analysis of chattering in systems with second-order sliding-modes. IEEE Trans. Automatic Control 52(11), 2085–2102 (2007)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Deza, F., Busvelle, E., Gauthier, J., Rakotopara, D.: High gain estimation for nonlinear systems. Systems & Control Letters 18(4), 295–299 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Ali, T.A., Postoyan, R., Lamnabhi-Lagarrigue, F.: Continuous discrete adaptive observers for state affine systems. Automatica 45(12) (2009)Google Scholar
  9. 9.
    Andrieu, V., Nadri, M.: Observer design for lipschitz systems with discrete-time measurements. In: Proc. 49th IEEE Conference on Decision and Control, Atlanta, GA, USA (2010)Google Scholar
  10. 10.
    Salgado, I., Moreno, J., Chairez, I.: Sampled output based continuous second order sliding mode observer. In: Proc. 11th International Workshop on Variable Structure Systems, Mexico City, Mexico (2010)Google Scholar
  11. 11.
    Salgado, I., Moreno, J., Chairez, I., Fridman, L.: Design of mixed luenberger and sliding continuous mode observer using sampled output information. In: Proc. 49th IEEE Conference on Decision and Control, Atlanta, GA, USA (2010)Google Scholar
  12. 12.
    Han, X., Fridman, E., Spurgeon, S.: A sliding mode observer for fault reconstruction under output sampling: A time-delay approach. In: Proc. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) Orlando, FL, USA (2011)Google Scholar
  13. 13.
    Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. of Control 58(6), 1247–1263 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of Intelligent Systems for Automation (CNR-ISSIA)National Research Council of ItalyGenoaItaly

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