On the stabilizability of homogeneous systems of odd degree
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 343-352.

We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.

DOI : 10.1051/cocv:2003016
Classification : 93D05, 93D15
Mots clés : asymptotic stabilization, nonlinear systems, homogeneous systems, stabilizability 
@article{COCV_2003__9__343_0,
     author = {Jerbi, Hamadi},
     title = {On the stabilizability of homogeneous systems of odd degree},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {343--352},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2003},
     doi = {10.1051/cocv:2003016},
     mrnumber = {1966537},
     zbl = {1063.93039},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2003016/}
}
TY  - JOUR
AU  - Jerbi, Hamadi
TI  - On the stabilizability of homogeneous systems of odd degree
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2003
SP  - 343
EP  - 352
VL  - 9
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2003016/
DO  - 10.1051/cocv:2003016
LA  - en
ID  - COCV_2003__9__343_0
ER  - 
%0 Journal Article
%A Jerbi, Hamadi
%T On the stabilizability of homogeneous systems of odd degree
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2003
%P 343-352
%V 9
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2003016/
%R 10.1051/cocv:2003016
%G en
%F COCV_2003__9__343_0
Jerbi, Hamadi. On the stabilizability of homogeneous systems of odd degree. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 343-352. doi : 10.1051/cocv:2003016. http://www.numdam.org/articles/10.1051/cocv:2003016/

[1] D. Ayels, Stabilization of a class of nonlinear systems by a smooth feedback. System Control Lett. 5 (1985) 181-191. | Zbl

[2] R.W. Brockett, Differentiel Geometric Control Theory, Chapter Asymptotic stability and feedback stabilization. Brockett, Milmann, Sussman (1983) 181-191. | MR | Zbl

[3] J. Carr, Applications of Center Manifold Theory. Springer Verlag, New York (1981). | MR | Zbl

[4] R. Chabour, G. Sallet and J.C. Vivalda, Stabilization of nonlinear two dimentional system: A bilinear approach. Math. Control Signals Systems (1996) 224-246. | MR | Zbl

[5] J.M. Coron, A Necessary Condition for Feedback Stabilization. System Control Lett. 14 (1990) 227-232. | MR | Zbl

[6] W. Hahn, Stability of Motion. Springer Verlag (1967). | MR | Zbl

[7] H. Hermes, Homogeneous Coordinates and Continuous Asymptotically Stabilizing Control laws, Differential Equations, Stability and Control, edited by S. Elaydi. Marcel Dekker Inc., Lecture Notes in Appl. Math. 10 (1991) 249-260. | MR | Zbl

[8] M.A. Krosnosel'Skii and P.P. Zabreiko Geometric Methods of Nonlinear Analysis. Springer Verlag, New York (1984).

[9] J.L. Massera, Contribution to stability theory. Ann. Math. 64 (1956) 182-206. | MR | Zbl

Cité par Sources :