Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 293-311.
@article{COCV_2000__5__293_0,
     author = {Faubourg, Ludovic and Pomet, Jean-Baptiste},
     title = {Control {Lyapunov} functions for homogeneous {{\textquotedblleft}Jurdjevic-Quinn{\textquotedblright}} systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {293--311},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     mrnumber = {1765428},
     zbl = {0959.93046},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2000__5__293_0/}
}
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
SP  - 293
EP  - 311
VL  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_2000__5__293_0/
LA  - en
ID  - COCV_2000__5__293_0
ER  - 
%0 Journal Article
%A Faubourg, Ludovic
%A Pomet, Jean-Baptiste
%T Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2000
%P 293-311
%V 5
%I EDP-Sciences
%U http://www.numdam.org/item/COCV_2000__5__293_0/
%G en
%F COCV_2000__5__293_0
Faubourg, Ludovic; Pomet, Jean-Baptiste. Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 293-311. http://www.numdam.org/item/COCV_2000__5__293_0/

[1] D. Aeyels, Stabilization of a class of nonlinear systems by smooth feedback control. Systems Control Lett. 5 ( 1985) 289-294. | MR | Zbl

[2] Z. Artstein, Stabilization with relaxed control. Nonlinear Anal. TMA 7 ( 1983) 1163-1173. | MR | Zbl

[3] A. Bacciotti, Local stabilizability of nonlinear control systems. World Scientifîc, Singapore, River Edge, London, Ser. Adv. Math. Appl. Sci. 8 ( 1992). | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR

[8] L. Faubourg, La déformation de fonctions de Lyapunov, Rapport de DEA d'automatique et informatique industrielle. INRIA-Université de Lille 1 ( 1997).

[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] 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. | MR | Zbl

[11] J.-P. Gauthier, Structure des Systèmes non-linéaires. Éditions du CNRS, Paris ( 1984). | MR | Zbl

[12] W. Hahn, Stability of Motion. Springer-Verlag, Berlin, New-York, Grundlehren Math. Wiss. 138 ( 1967). | MR | Zbl

[13] V. Jurdjevic and J.P. Quinn, Controllability and stability. J. Differential Equations 28 ( 1978) 381-389. | MR | Zbl

[14] M. Kawski, Homogeneous stabilizing feedback laws. Control Theory and Adv. Technol. 6 ( 1990), 497-516. | MR

[15] H.K. Khalil, Nonlinear Systems. MacMillan, New York, Toronto, Singapore ( 1992). | MR | Zbl

[16] J. Kurzweil, On the inversion of Ljapunov's second theorem on stability of motion. AMS Trans., Ser. II 24 ( 1956) 19-77. | Zbl

[17] J.-P. Lasalle, Stability theory for ordinary differential equations. J. Differential Equations 4 ( 1968) 57-65. | MR | Zbl

[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] F. Mazenc, Stabilisation de trajectoires, ajout d'intégration, commandes saturées, Thèse de doctorat. École des Mines de Paris ( 1989).

[20] P. Morin, Robust stabilization of the angular velocity of a rigid body with two actuators. European J. Control 2 ( 1996) 51-56. | Zbl

[21] R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited. Systems Control Lett. 18 ( 1992) 93-98. | MR | Zbl

[22] G. Sallet, Historique des techniques de Jurdjevic-Quinn(private communication).

[23] R. Sépulchre, M. Janković and P.V. Kokotović, Constructive Nonlinear Control. Springer-Verlag, Comm. Control Engrg. Ser. ( 1997). | MR | Zbl

[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. | MR | Zbl

[25] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 1. Publish or Perish, Houston, second Ed. ( 1979). | Zbl

[26] J. Tsinias, Remarks on feedback stabilizability of homogeneous systems. Control Theory and Adv. Technol. 6 ( 1990) 533-542. | MR

[27] J. Zhao and I. Kanellakopoulos, Flexible back-stepping design for tracking and disturbance attenuation. Internat J. Robust Nonlinear Control 8 ( 1998) 331-348. | MR | Zbl