# Controllability of right invariant systems on semi-simple Lie groups

R. El Assoudi; J. Gauthier; I. Kupka

Banach Center Publications (1995)

- Volume: 32, Issue: 1, page 199-208
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topEl Assoudi, R., Gauthier, J., and Kupka, I.. "Controllability of right invariant systems on semi-simple Lie groups." Banach Center Publications 32.1 (1995): 199-208. <http://eudml.org/doc/262629>.

@article{ElAssoudi1995,

abstract = {We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.},

author = {El Assoudi, R., Gauthier, J., Kupka, I.},

journal = {Banach Center Publications},

keywords = {invariant vector fields; controllability; root systems; semi-simple Lie algebras; Lie saturate; rank condition; right invariant; Lie group},

language = {eng},

number = {1},

pages = {199-208},

title = {Controllability of right invariant systems on semi-simple Lie groups},

url = {http://eudml.org/doc/262629},

volume = {32},

year = {1995},

}

TY - JOUR

AU - El Assoudi, R.

AU - Gauthier, J.

AU - Kupka, I.

TI - Controllability of right invariant systems on semi-simple Lie groups

JO - Banach Center Publications

PY - 1995

VL - 32

IS - 1

SP - 199

EP - 208

AB - We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.

LA - eng

KW - invariant vector fields; controllability; root systems; semi-simple Lie algebras; Lie saturate; rank condition; right invariant; Lie group

UR - http://eudml.org/doc/262629

ER -

## References

top- [B] N. Bourbaki, Groupes et algèbres de Lie, Fasc. XXXVIII, chap. 7-8, Hermann, Paris, 1975. Zbl0329.17002
- [BJKS] B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of families of invariant vector fields on the semi-direct products of Lie groups, Trans. Amer. Math. Soc. 271 (1982), 525-535. Zbl0519.49023
- [EA] R. El Assoudi, Accessibilité par des champs de vecteurs invariants à droite sur un groupe de Lie, Thèse de doctorat de l'Université Joseph Fourier, Grenoble, 1991.
- [EAG] R. El Assoudi and J. P. Gauthier, Controllability of right invariant systems on real simple Lie groups of type ${F}_{4}$, ${G}_{2}$, ${B}_{n}$ and ${C}_{n}$, Math. Control Signals Systems 1 (1988), 293-301.
- [EAGK] R. El Assoudi, J. P. Gauthier and I. Kupka, Controllability of right invariant systems on semi-simple Lie groups, Ann. Inst. Henri Poincaré, to appear. Zbl0839.93019
- [GB] J. P. Gauthier et G. Bornard, Controllabilité des systèmes bilinéaires, SIAM J. Control Optim. 20 (1982), 377-384. Zbl0579.93005
- [GKS] J. P. Gauthier, I. Kupka and G. Sallet, Controllability of right invariant systems on real simple Lie groups, Systems Control Letters 5 (1984), 187-190. Zbl0552.93010
- [H] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. Zbl0111.18101
- [HHL] J. Hilgert, K. Hoffman and J. D. Lawson, Controllability of systems on a nilpotent Lie group, Beitr. Algebra Geom. 30 (1985), 185-190.
- [HI] J. Hilgert, Max. semigroups and controllability in products of Lie groups, Arch. Math. (Basel) 49 (1987), 189-195. Zbl0649.22003
- [J] A. Joseph, The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Sci. Ecole Norm. Sup. (4) 9 (1976), 1-29. Zbl0346.17008
- [JK] V. Jurdjevic and I. Kupka, Controllability of right invariant systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier (Grenoble) 31 (4) (1981), 151-179. Zbl0453.93011
- [L] J. D. Lawson, Maximal subsemigroups of Lie groups that are total, Proc. Edinburgh Math. Soc. 30 (1987), 479-501. Zbl0649.22004
- [LC] F. S. Leite and P. E. Crouch, Controllability on classical Lie groups, Math. Control Signals Systems 1, 1988, 31-42. Zbl0658.93013
- [W] G. Warner, Harmonic Analysis on Semi-simple Lie Groups 1, Springer, Berlin, 1972. Zbl0265.22020

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.