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Bibliography

1
BUIUM (Alexandru), Differential algebra and diophantine geometry, Actualités Mathématiques, Hermann, Paris, 1994.

2
Charlet (B.), Lévine (J.) and Marina (R.), «Sufficient Conditions for Dynamic State Feedback Linearization» Siam J. Control & Optimiz. 29, p. 38-57, 1991.

3
COHN (Richard M.), «The Greenspan bound for the order of differential systems», Proc. Amer. Math. Soc. 79 (1980), n$^{\circ}$ 4, 523-526.

4
COHN (Richard M.), «Order and dimension», Proc. Amer. Math. Soc. 87 (1983), n$^{\circ}$ 1, 1-6.

5
FLIESS (Michel), LÉVINE (Jean), MARTIN (Philippe) et ROUCHON (Pierre), ``Flatness and defect of nonlinear systems: introductory theory and applications'', Internat. J. Control, 61, 1995, p. 1327-1887.

6
FLIESS (Michel), LÉVINE (Jean), MARTIN (Philippe), OLLIVIER (François) et ROUCHON (Pierre), ``Flatness and dynamic feedback linearizability: two approaches'' Proceedings of the 3rd European Control Conference, 1995. pp. 649- 654.

7
JACOBI (Carl Gustav Jacob), «De investigando ordine systematis aequationum differentialum vulgarium cujuscunque », published by C. W. Borchardt, Borchardt Journal für die reine und angewandte Mathematik, Bd 64, p. 297-320, reproduced in C.G.J. Jacobi's gesammelte Werke, fünfter Band, herausgegeben von K. Weierstrass, Berlin, Bruck und Verlag von Georg Reimer, 1890, p. 193-216. French translation available at url: http://www.stix.polytechnique.fr/~ ollivier/JACOBI/ordreSysteme/ordreSysteme.html

8
JACOBI (Carl Gustav Jacob), «De aequationum differentialum systemate non normali ad formam normalem revocando», published by A. Clebsch, reproduced in C.G.J. Jacobi's gesammelte Werke, fünfter Band, herausgegeben von K. Weierstrass, Berlin, Bruck und Verlag von Georg Reimer, 1890, p. 485-513. French translation available at url:
http://www.stix.polytechnique.fr/~ ollivier/JACOBI/reductionFormeNormale/reductionFormeNormale.html

9
OLLIVIER (François), «Une réponse négative au problème de Lüroth différentiel en dimension 2», C. R. Acad. Sci. Paris, t. 327, Série I. p. 881-886, 1998.

10
RITT, (Joseph Fels), «Jacobi's problem on the order of a system of differential equations », Annals of Mathematics, vol. 36, 1935, 303-312.

11
RITT (Joseph Fels), Differential Algebra, Amer. Math. Soc. Colloq. Publ.,vol. 33, A.M.S., New-York, 1950.

12
PEREIRA DA SILVA (Paulo Sérgio) et ROUCHON (Pierre) «On time-invariant systems possessing time-dependent flat outputs», actes de NOLCOS 2004, Elsevier, 2004.



Francois Ollivier 2004-11-15