We construct explicitly an homogeneous feedback for a class of single input, two dimensional and homogeneous systems.
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] Stabilization of a class of nonlinear systems by a smooth feedback. System Control Lett. 5 (1985) 181-191. | Zbl
,[2] Differentiel Geometric Control Theory, Chapter Asymptotic stability and feedback stabilization. Brockett, Milmann, Sussman (1983) 181-191. | MR | Zbl
,[3] Applications of Center Manifold Theory. Springer Verlag, New York (1981). | MR | Zbl
,[4] Stabilization of nonlinear two dimentional system: A bilinear approach. Math. Control Signals Systems (1996) 224-246. | MR | Zbl
, and ,[5] A Necessary Condition for Feedback Stabilization. System Control Lett. 14 (1990) 227-232. | MR | Zbl
,[6] Stability of Motion. Springer Verlag (1967). | MR | Zbl
,[7] 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]
and of Nonlinear Analysis. Springer Verlag, New York (1984).[9] Contribution to stability theory. Ann. Math. 64 (1956) 182-206. | MR | Zbl
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