Adaptive feedback passivity of nonlinear systems with sliding mode

  • Ali J. Koshkouei
  • Alan S. I. Zinober
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 281)


Passivity of a class of nonlinear systems with unknown parameters is studied in this paper. There is a close connection between passivity and Lyapunov stability. This relationship can be shown by employing a storage function as a Lyapunov function. Passivity is the property stating that any storage energy in a system is not larger than the energy supplied to it from external sources. An appropriate update law is designed so that the new transformed system is passive. Sliding mode control is designed to maintain trajectories of a passive system on the sliding hyperplane and eventually to an equilibrium point on this surface.


Nonlinear System Slide Mode Control Sliding Mode Passive System Storage Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Byrnes, C. I., Isidori, A., Willems, J. C. (1991) Passivity, feedback equivalence and global stabilization of minimum phase nonlinear systems. IEEE Trans. Automat. Control, 36, 1228–1240zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hill, D., Moylan, P. (1976) The stability of nonlinear dissipative systems. IEEE Trans. Automat. Control, 21, 708–711zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hill, D. and Moylan, P. (1997) Stability results for nonlinear feedback systems. Automatica, 13, 377–382CrossRefGoogle Scholar
  4. 4.
    Ríos-Bolívar, M., Acosta-Contreras, V., Sira-Ramírez, H. (2000) Adaptive passivation of a class of uncertain nonlinear system. Proc. 39th Conference on Decision and Control, SydneyGoogle Scholar
  5. 5.
    Ríos-Bolívar, M., Zinober, A. S. I. (1999) Dynamical adaptive sliding mode control of observable minimum phase uncertain nonlinear systems. In: “Variable Structure Systems: Variable structure systems, sliding mode and nonlinear control, (Editors: Young and Özgüner), Springer-Verlag, London, 211–236CrossRefGoogle Scholar
  6. 6.
    Ortega, R. (1991) Passivity properties for stabilizing of cascaded nonlinear systems. Automatica, 27, 423–424zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ortega, R., Spong, M. (1989) Adaptive motion control of rigid robots: a tutorial. Automatica, 25, 877–888zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ortega, R., Nicklasson, P., Sira-Ramírez, H. (1998) The Passivity Based Control of Euler-Lagrange Systems. Springer-Verlag, LondonGoogle Scholar
  9. 9.
    Sepulchre, R., Janković, M., Kokotović, P. (1997) Constructive Nonlinear Control. Springer-Verlag, LondonzbMATHGoogle Scholar
  10. 10.
    Sira-Ramírez, H. (1998) A general canonical form for feedback passivity of nonlinear systems. Int. J. Control, 71, 891–905zbMATHCrossRefGoogle Scholar
  11. 11.
    Sira-Ramírez, H., Ríos-Bolívar, M. (1999) Feedback passivity of nonlinear multivariable systems. Proc. 14th World Congress of IFAC, Beijing, 73–78Google Scholar
  12. 12.
    Slotine, J.-J. E., Li, W. (1991) Applied nonlinear control. Prentice Hall, LondonzbMATHGoogle Scholar
  13. 13.
    Willems, J. C.(1971) The analysis of feedback systems. MIT Press, Cambridge, MAzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ali J. Koshkouei
    • 1
  • Alan S. I. Zinober
    • 1
  1. 1.Department of Applied MathematicsThe University of SheffieldSheffieldUK

Personalised recommendations