On the stabilizability of homogeneous systems of odd degree
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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
Keywords: asymptotic stabilization, nonlinear systems, homogeneous systems, stabilizability
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     title = {On the stabilizability of homogeneous systems of odd degree},
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Jerbi, Hamadi. On the stabilizability of homogeneous systems of odd degree. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 343-352. doi : 10.1051/cocv:2003016. http://archive.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

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