Geodesic
Controllability of invariant control systems at uniform time
Kybernetika, Tome 45 (2009) no. 3, pp. 405-416.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{KYB_2009__45_3_a2,
     author = {Ayala, V{\'\i}ctor and Ayala-Hoffmann, Jos\'e and Azevedo Tribuzy, Ivan de},
     title = {Controllability of invariant control systems at uniform time},
     journal = {Kybernetika},
     pages = {405--416},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2009},
     mrnumber = {2543130},
     zbl = {1165.93301},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_3_a2/}
}
TY  - JOUR
AU  - Ayala, Víctor
AU  - Ayala-Hoffmann, José
AU  - Azevedo Tribuzy, Ivan de
TI  - Controllability of invariant control systems at uniform time
JO  - Kybernetika
PY  - 2009
SP  - 405
EP  - 416
VL  - 45
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2009__45_3_a2/
LA  - en
ID  - KYB_2009__45_3_a2
ER  - 
%0 Journal Article
%A Ayala, Víctor
%A Ayala-Hoffmann, José
%A Azevedo Tribuzy, Ivan de
%T Controllability of invariant control systems at uniform time
%J Kybernetika
%D 2009
%P 405-416
%V 45
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2009__45_3_a2/
%G en
%F KYB_2009__45_3_a2
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/