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Jurdjevic, V.; Kupka, I.

Control systems on semi-simple Lie groups and their homogeneous spaces. (English) Zbl 0453.93011

Ann. Inst. Fourier 31, No. 4, 151-179 (1981).
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Cited in 51 Documents

MSC:

93B05 Controllability
93C10 Nonlinear systems in control theory
58B25 Group structures and generalizations on infinite-dimensional manifolds
37N99 Applications of dynamical systems
22E46 Semisimple Lie groups and their representations

Keywords:

semi-simple Lie group; bilinear systems; semi-algebraic condition
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\textit{V. Jurdjevic} and \textit{I. Kupka}, Ann. Inst. Fourier 31, No. 4, 151--179 (1981; Zbl 0453.93011)
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References:

[1] N. BOURBAKI, Algèbre de Lie, Chap. VII-VIII, Hermann.
[2] A. BOREL-G. MOSTOW, On semi-simple automorphisms of Lie algebras, Ann. of Math., vol. 61 (1955), 389-405. · Zbl 0066.02401
[3] J. DIXMIER, Enveloping algebras, North-Holland. · Zbl 0867.17001
[4] H. FREUDENTHAL, Linear Lie groups, Academic Press. · Zbl 0377.22001
[5] V. JURDJEVIC and I. KUPKA, Control systems subordinated to a group action : accessibility, Journal of Diff. Equations, 39, 2 (1981), 186-211. · Zbl 0531.93008
[6] V. JURDJEVIC and H. SUSSMANN, Control systems on Lie groups, Journal of Diff. Equations, (12) (1972), 313-329. · Zbl 0237.93027
[7] A. KRENER, A generalization of Chow’s theorem and the bang-bang theorem to non-linear control systems, SIAM J. Control, 11 (1973), 670-676. · Zbl 0243.93009
[8] C. LOBRY, Contrôlabilité des systèmes non-linéaires, SIAM Journal on Control, 8 (1970), 573-605. · Zbl 0207.15201
[9] C. LOBRY, Contrôlabilité des systèmes non-linéaires, Proceedings of űoutils et modèles mathématiques pour l’automatique et l’analyse de systèmesƈ, C.N.R.S., Mai 1980, Centre Paul Langevin (CAES-CNRS), Aussois, France.
[10] B. LEVITT and H. SUSSMANN, On controllability by means of two vector fields, SIAM Journal on Control, 13 (1975), 1271-1281. · Zbl 0313.93006
[11] G. MOSTOW, Lie algebras and Lie groups, Mem. Amer. Math. Soc., n° 14.
[12] H. SUSSMANN and V. JURDJEVIC, Controllability of non-linear systems, Journal of Diff. Equations, 12 (1972), 95-116. · Zbl 0242.49040
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