Controllability of right invariant systems on semi-simple Lie groups
El Assoudi, R. ; Gauthier, J. ; Kupka, I.
Banach Center Publications, Tome 31 (1995), p. 199-208 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262629 
@article{bwmeta1.element.bwnjournal-article-bcpv32z1p199bwm,
     author = {El Assoudi, R. and Gauthier, J. and Kupka, I.},
     title = {Controllability of right invariant systems on semi-simple Lie groups},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {199-208},
     zbl = {0839.93019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p199bwm}
}

El Assoudi, R.; Gauthier, J.; Kupka, I. Controllability of right invariant systems on semi-simple Lie groups. Banach Center Publications, Tome 31 (1995) pp. 199-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p199bwm/

[000] [B] N. Bourbaki, Groupes et algèbres de Lie, Fasc. XXXVIII, chap. 7-8, Hermann, Paris, 1975. | Zbl 0329.17002

[001] [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. | Zbl 0519.49023

[002] [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.

[003] [EAG] R. El Assoudi and J. P. Gauthier, Controllability of right invariant systems on real simple Lie groups of type F4, G2, Bn and Cn, Math. Control Signals Systems 1 (1988), 293-301.

[004] [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. | Zbl 0839.93019

[005] [GB] J. P. Gauthier et G. Bornard, Controllabilité des systèmes bilinéaires, SIAM J. Control Optim. 20 (1982), 377-384. | Zbl 0579.93005

[006] [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. | Zbl 0552.93010

[007] [H] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962. | Zbl 0111.18101

[008] [HHL] J. Hilgert, K. Hoffman and J. D. Lawson, Controllability of systems on a nilpotent Lie group, Beitr. Algebra Geom. 30 (1985), 185-190.

[009] [HI] J. Hilgert, Max. semigroups and controllability in products of Lie groups, Arch. Math. (Basel) 49 (1987), 189-195. | Zbl 0649.22003

[010] [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. | Zbl 0346.17008

[011] [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. | Zbl 0453.93011

[012] [L] J. D. Lawson, Maximal subsemigroups of Lie groups that are total, Proc. Edinburgh Math. Soc. 30 (1987), 479-501. | Zbl 0649.22004

[013] [LC] F. S. Leite and P. E. Crouch, Controllability on classical Lie groups, Math. Control Signals Systems 1, 1988, 31-42. | Zbl 0658.93013

[014] [W] G. Warner, Harmonic Analysis on Semi-simple Lie Groups 1, Springer, Berlin, 1972. | Zbl 0265.22020