Décompositions en cascades des systèmes automatiques et feuilletages invariants
Fliess, Michel
Bulletin de la Société Mathématique de France, Tome 113 (1985), p. 285-293 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{BSMF_1985__113__285_0,
     author = {Fliess, Michel},
     title = {D\'ecompositions en cascades des syst\`emes automatiques et feuilletages invariants},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     volume = {113},
     year = {1985},
     pages = {285-293},
     doi = {10.24033/bsmf.2034},
     mrnumber = {88f:93033},
     zbl = {0587.93031},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/BSMF_1985__113__285_0}
}

Fliess, Michel. Décompositions en cascades des systèmes automatiques et feuilletages invariants. Bulletin de la Société Mathématique de France, Tome 113 (1985) pp. 285-293. doi : 10.24033/bsmf.2034. http://gdmltest.u-ga.fr/item/BSMF_1985__113__285_0/

[1] Cartan (E.). - Les groupes de transformations continus, infinis, simples, Ann. Scient. Éc. Norm. Sup., t. 26, 1909, p. 93-161 (œuvres complètes, partie II, p. 857-925, C.N.R.S., Paris, 1984). | JFM 40.0193.02 | Numdam

[2] Claude (D.), Fliess (M.) et Isidori (A.). - Immersion, directe et par bouclage, d'un système non linéaire dans un linéaire, C.R. Acad. Sc., t. 296, 1983, série I, p. 237-240. | MR 84c:58074 | Zbl 0529.93030

[3] Eilenberg (S.). - Automata, Languages and Machines, vol. B, Academic Press, New York, 1976. | MR 58 #26604b | Zbl 0359.94067

[4] Fliess (M.). - Réalisation locale des systèmes non linéaires, algèbres de Lie filtrées transitives et séries génératrices non commutatives, Invent. Math., vol. 71, 1983, p. 521-537. | MR 85k:93020 | Zbl 0513.93014

[5] Fliess (M.). - Cascade decompositions of nonlinear systems, foliations and ideals of transitive Lie algebras, Systems Control Lett., vol. 5, 1984/1985, p. 263-265. | MR 86h:93034 | Zbl 0562.93040

[6] Fliess (M.). - Cascade decompositions, invariant foliations and ideals of Lie algebras, Proc. 24th I.E.E.E. Control Decision Conf., Fort Lauderdale, FL, 1985.

[7] Fliess (M.) and Kupka (I.). - A finiteness criterion for nonlinear input-output differential systems, S.I.A.M.J. Control Optimiz., vol. 21, 1983, p. 721-728. | MR 85i:93009 | Zbl 0529.93031

[8] Grizzle (J. W.) and Marcus (S. I.). - The structure of nonlinear control systems possessing symmetries, I.E.E.E. Trans. Automatic Control, vol. 30, 1985, p. 248-258. | MR 86e:93030 | Zbl 0562.93041

[9] Guillemin (V.). - A Jordan-Hölder decomposition for a certain class of infinite-dimensional Lie algebras, J. Differential Geometry, vol. 2, 1968, p. 313-345. | MR 41 #8481 | Zbl 0183.26102

[10] Hermann (R.) and Krener (A. J.). - Nonlinear controllability and observability, I.E.E.E. Trans. Automatic Control, vol. 22, 1977, p. 728-740. | MR 57 #15597 | Zbl 0396.93015

[11] Isidori (A.). - Nonlinear control systems: an introduction, Lect. Notes Control Informat. Sc., vol. 72, Springer-Verlag, Berlin, 1985. | MR 88f:93003 | Zbl 0569.93034

[12] Isidori (A.), Krener (A. J.), Gori-Giorgi (C.) and Monaco (S.). - Nonlinear decoupling via feedback: a differential geometric approach, I.E.E.E. Trans. Automatic Control, vol. 26, 1981, p. 331-345. | MR 82e:93052 | Zbl 0481.93037

[13] Krener (A. J.). - A decomposition theory for differentiable systems, S.I.A.M. J. Control Optimiz., vol. 15, 1977, p. 813-829. | MR 57 #18906 | Zbl 0361.93023

[14] Krohn (K.) and Rhodes (J. L.). - Algebraic theory of machines, I. Prime decomposition theorem for finite semigroups and machines, Trans. Amer. Math. Soc., vol. 116, 1965, p. 450-464. | MR 32 #5755 | Zbl 0148.01002

[15] Kumpera (A.). - Suites de Jordan-Hölder et principales d'un groupe de Lie, J. Differential Geometry, vol. 15, 1980, p. 307-353. | MR 83a:22017 | Zbl 0483.22006

[16] Molino (P.). - Théorie des G-structures: le problème d'équivalence, Lect. Notes Math. 588, Springer-Verlag, Berlin, 1977. | MR 58 #24419 | Zbl 0357.53022

[17] Nagano (T.). - Linear differential systems with singularities and an application to tansitive Lie algebras, J. Math. Soc. Japan, vol. 18, 1966, p. 398-404. | MR 33 #8005 | Zbl 0147.23502

[18] Nijmeijer (H.) et Van Der Schaft (A. J.). - Partial symmetries for nonlinear systems, Math. Systems Theory, vol. 18, 1985, p. 79-96. | MR 86k:93071 | Zbl 0585.93029

[19] Pommaret (J. F.). - Differential Galois Theory, Gordon and Breach, New York, 1983. | Zbl 0539.12013

[20] Respondek (W.). - On decomposition of nonlinear control systems, Systems Control Lett., vol. 1, 1982, p. 301-308. | MR 83m:93032 | Zbl 0499.93030

[21] Rodrigues (A. M.). - Sur le noyau d'un pseudo-groupe de Lie infinitésimal involutif transitif par rapport à une fibration invariante, C.R. Acad. Sc., t. 269, 1969, série A, p. 1154-1155. | MR 41 #2722 | Zbl 0194.52704

[22] Singer (I. M.) and Sternberg (S.). - The infinite groups of Lie and Cartan, I, J. Analyse Math., vol. 15, 1965, p. 1-114. | MR 36 #911 | Zbl 0277.58008

[23] Sussmann (H. J.). - Lie brackets, real analyticity and geometric control, in Differential Geometric Control Theory, R. W. BROCKETT, R. S. MILMAN and H. J. SUSSMANN, Eds., p. 1-116, Birkhäuser, Boston, 1983. | MR 85e:93010 | Zbl 0545.93002