Geodesic
Controllability of invariant control systems at uniform time
Kybernetika, Tome 45 (2009) no. 3, pp. 405-416 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $G$ be a compact and connected semisimple Lie group and $\Sigma $ an invariant control systems on $G$. Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time $s_{\Sigma }$ such that the system turns out controllable at uniform time $s_{\Sigma }$. Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if $ A=\bigcap _{ t > 0}A(t,e)$ denotes the reachable set from arbitrary uniform time, we conjecture that it is possible to determine $A$ as the intersection of the isotropy groups of orbits of $G$-representations which contains $\exp (\mathfrak{z})$, where $\mathfrak{z}$ is the Lie algebra determined by the control vectors.
Let $G$ be a compact and connected semisimple Lie group and $\Sigma $ an invariant control systems on $G$. Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time $s_{\Sigma }$ such that the system turns out controllable at uniform time $s_{\Sigma }$. Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if $ A=\bigcap _{ t > 0}A(t,e)$ denotes the reachable set from arbitrary uniform time, we conjecture that it is possible to determine $A$ as the intersection of the isotropy groups of orbits of $G$-representations which contains $\exp (\mathfrak{z})$, where $\mathfrak{z}$ is the Lie algebra determined by the control vectors.
Classification : 22E15, 93B05, 93C25
Keywords: uniform-time; compact; semisimple; reverse-system 
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     title = {Controllability of invariant control systems at uniform time},
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Ayala, Víctor; Ayala-Hoffmann, José; Azevedo Tribuzy, Ivan de. Controllability of invariant control systems at uniform time. Kybernetika, Tome 45 (2009) no. 3, pp. 405-416. http://geodesic.mathdoc.fr/item/KYB_2009_45_3_a2/

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