Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems

Ludovic Faubourg; Jean-Baptiste Pomet

ESAIM: Control, Optimisation and Calculus of Variations (2000)

  • Volume: 5, page 293-311
  • ISSN: 1292-8119

How to cite

top

Faubourg, Ludovic, and Pomet, Jean-Baptiste. "Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems." ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 293-311. <http://eudml.org/doc/90572>.

@article{Faubourg2000,
author = {Faubourg, Ludovic, Pomet, Jean-Baptiste},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {feedback stabilization; control Lyapunov functions; Lyapunov design},
language = {eng},
pages = {293-311},
publisher = {EDP Sciences},
title = {Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems},
url = {http://eudml.org/doc/90572},
volume = {5},
year = {2000},
}

TY - JOUR
AU - Faubourg, Ludovic
AU - Pomet, Jean-Baptiste
TI - Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2000
PB - EDP Sciences
VL - 5
SP - 293
EP - 311
LA - eng
KW - feedback stabilization; control Lyapunov functions; Lyapunov design
UR - http://eudml.org/doc/90572
ER -

References

top
  1. [1] D. Aeyels, Stabilization of a class of nonlinear systems by smooth feedback control. Systems Control Lett. 5 ( 1985) 289-294. Zbl0569.93056MR791542
  2. [2] Z. Artstein, Stabilization with relaxed control. Nonlinear Anal. TMA 7 ( 1983) 1163-1173. Zbl0525.93053MR721403
  3. [3] A. Bacciotti, Local stabilizability of nonlinear control systems. World Scientifîc, Singapore, River Edge, London, Ser. Adv. Math. Appl. Sci. 8 ( 1992). Zbl0757.93061MR1148363
  4. [4] R.W. Brockett, Asymptotic stability and feedback stabilization, in Differential Geometric Control Theory, edited by R.W. Brockett, R.S. Millman and H.J. Sussmann. Basel-Boston, Birkäuser ( 1983) 181-191. Zbl0528.93051MR708502
  5. [5] R.T. Bupp, D.S. Bernstein and V.T. Coppola, A benchmark problem for nonlinear control design. Internat J. Robust Nonlinear Control 8 ( 1998) 307-310. MR1611573
  6. [6] R.T. Bupp, D.S. Bernstein and V.T. Coppola, Experimental implementation of integrator back-stepping and passive nonlinear controllers on the RTAC testbed. Internat J. Robust Nonlinear Control 8 ( 1998) 435-457. Zbl0925.93352MR1611580
  7. [7] J.-M. Coron, L. Praly and A.R. Teel, Feedback stabilization of nonlinear system: Sufficient conditions and lyapunov and input-output techniques, in Trends in Control, a European Perspective, edited by A. Isidori. Springer-Verlag ( 1995) 283-348. MR1448452
  8. [8] L. Faubourg, La déformation de fonctions de Lyapunov, Rapport de DEA d'automatique et informatique industrielle. INRIA-Université de Lille 1 ( 1997). 
  9. [9] L. Faubourg and J.-B. Pomet, Strict control Lyapunov functions for homogeneous Jurdjevic-Quinn type systems, in Nonlinear Control Systems Design Symposium (NOLCOS'98), edited by H. Huijberts, H. Nijmeijer, A. van der Schaft and J. Scherpen. IFAC ( 1998) 823-829. 
  10. [10] L. Faubourg and J.-B. Pomet, Design of control Lyapunov functions for "Jurdjevic-Quinn" systems, in Stability and Stabilization of Nonlinear Systems, edited by D. Aeyels et al. Springer-Verlag, Lecture Notes in Contr. & Inform. Sci. ( 1999) 137-150. Zbl0945.93607MR1714587
  11. [11] J.-P. Gauthier, Structure des Systèmes non-linéaires. Éditions du CNRS, Paris ( 1984). Zbl0606.58001MR767635
  12. [12] W. Hahn, Stability of Motion. Springer-Verlag, Berlin, New-York, Grundlehren Math. Wiss. 138 ( 1967). Zbl0189.38503MR223668
  13. [13] V. Jurdjevic and J.P. Quinn, Controllability and stability. J. Differential Equations 28 ( 1978) 381-389. Zbl0417.93012MR494275
  14. [14] M. Kawski, Homogeneous stabilizing feedback laws. Control Theory and Adv. Technol. 6 ( 1990), 497-516. MR1092775
  15. [15] H.K. Khalil, Nonlinear Systems. MacMillan, New York, Toronto, Singapore ( 1992). Zbl0969.34001MR1201326
  16. [16] J. Kurzweil, On the inversion of Ljapunov's second theorem on stability of motion. AMS Trans., Ser. II 24 ( 1956) 19-77. Zbl0127.30703
  17. [17] J.-P. LaSalle, Stability theory for ordinary differential equations. J. Differential Equations 4 ( 1968) 57-65. Zbl0159.12002MR222402
  18. [18] W. Liu, Y. Chitour and E. Sontag, Remarks on finite gain stabilizability of linear systems subject to input saturation, in 32th IEEE Conf. on Decision and Control. San Antonio, USA ( 1993) 1808-1813. 
  19. [19] F. Mazenc, Stabilisation de trajectoires, ajout d'intégration, commandes saturées, Thèse de doctorat. École des Mines de Paris ( 1989). 
  20. [20] P. Morin, Robust stabilization of the angular velocity of a rigid body with two actuators. European J. Control 2 ( 1996) 51-56. Zbl0858.93057
  21. [21] R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited. Systems Control Lett. 18 ( 1992) 93-98. Zbl0743.93082MR1149353
  22. [22] G. Sallet, Historique des techniques de Jurdjevic-Quinn(private communication). 
  23. [23] R. Sépulchre, M. Janković and P.V. Kokotović, Constructive Nonlinear Control. Springer-Verlag, Comm. Control Engrg. Ser. ( 1997). Zbl1067.93500MR1481435
  24. [24] E.D. Sontag, Feedback stabilization of nonlinear systems, in Robust control of linear systems and nonlinear control, Vol. 2 of proceedings of MTNS'89, edited by M.A. Kaashoek, J.H. van Schuppen and A. Ran. Basel-Boston, Birkhäuser ( 1990) 61-81. Zbl0735.93063MR1115377
  25. [25] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 1. Publish or Perish, Houston, second Ed. ( 1979). Zbl0439.53005
  26. [26] J. Tsinias, Remarks on feedback stabilizability of homogeneous systems. Control Theory and Adv. Technol. 6 ( 1990) 533-542. MR1092777
  27. [27] J. Zhao and I. Kanellakopoulos, Flexible back-stepping design for tracking and disturbance attenuation. Internat J. Robust Nonlinear Control 8 ( 1998) 331-348. Zbl0925.93824MR1611575

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.