Semi-groupes intégraux de SL(2,\({\mathbb{R}})\). Application à la théorie du contrôle. (Integral semigroups on SL(2,\({\mathbb{R}})\). Application to control theory). (French) Zbl 0602.93005

The subject of this work is the controllability problem for a family F of right invariant vector fields on the standard Lie group SL(2,\({\mathbb{R}})\). In particular, it is proven that F is controllable if and only if one of the following two cases occurs:
1) the cones generated by F and -F coincide and \(Lie(F)=sl(2,{\mathbb{R}});\)
2) the cones generated by F and -F differ but the cone generated by F contains a compact element.
The main result is applied to the controllability problem on \(GL^+(2,{\mathbb{R}})\), on \(S^ 1\) and on \({\mathbb{R}}^ 2\setminus \{0\}\).
Reviewer: A.Bacciotti


93B05 Controllability
93B03 Attainable sets, reachability
93C10 Nonlinear systems in control theory
22E99 Lie groups