R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, Tensor Analysis and Applications, 1983.
DOI : 10.1007/978-1-4612-1029-0

M. D. Di-benedetto, J. H. Grizzle, and C. H. Moog, Rank Invariants of Nonlinear Systems, SIAM Journal on Control and Optimization, vol.27, issue.3, pp.658-672, 1989.
DOI : 10.1137/0327035

R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior Differential Systems, 1991.
DOI : 10.1007/978-1-4613-9714-4

B. Charlet, J. Lévine, and R. Marino, On dynamic feedback linearization, Systems & Control Letters, vol.13, issue.2, pp.743-151, 1989.
DOI : 10.1016/0167-6911(89)90031-5

B. Charlet, J. Lévine, and R. Marino, Sufficient Conditions for Dynamic State Feedback Linearization, SIAM Journal on Control and Optimization, vol.29, issue.1, pp.38-57, 1991.
DOI : 10.1137/0329002

M. Fliess, J. Lévine, . Ph, P. Martin, and . Rouchon, Défaut d'un système non linéaire et commande haute fréquence, C.R. Acad. Sc. Paris, issue.I, p.316, 1993.

M. Fliess, J. Lévine, . Ph, P. Martin, and . Rouchon, On differentially flat non linear systems, Proceedings of IFAC NOLCOS Conf, 1992.

M. Fliess, J. Lévine, . Ph, P. Martin, and . Rouchon, Sur les systèmes nonlinéaires différentiellement plats, C.R. Acad. Sc. Paris, issue.I, pp.315619-624, 1992.

L. R. Hunt, R. Su, and G. Meyer, Design for multi-input nonlinear systems, Differential Geometric Control Theory, pp.268-298, 1983.

B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Pol. Sci., Ser. Sci. Math, vol.28, pp.9-10517, 1980.

R. Marino, On the largest feedback linearizable subsystem, Systems & Control Letters, vol.6, issue.5, pp.345-351, 1986.
DOI : 10.1016/0167-6911(86)90130-1

. Ph and . Martin, ContributionàContributionà l'´ etude des systèmes différentiellement plats, 1992.

. Ph and . Martin, An intrinsic condition for regular decoupling, To appear in Systems and Control Letters, 1993.

C. H. Moog, Nonlinear decoupling and structure at infinity, Mathematics of Control, Signals, and Systems, vol.35, issue.3, pp.275-268, 1988.
DOI : 10.1007/BF02551287

H. Nijmeijer, A. J. Van, and . Schaft, Controlled invariance for nonlinear systems, IEEE Transactions on Automatic Control, vol.27, issue.4, pp.904-914, 1982.
DOI : 10.1109/TAC.1982.1103025

J. F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, 1978.

W. F. Shadwick, Absolute equivalence and dynamic feedback linearization, Systems & Control Letters, vol.15, issue.1, pp.35-39, 1990.
DOI : 10.1016/0167-6911(90)90041-R

R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior Differential Systems, 1991.
DOI : 10.1007/978-1-4613-9714-4

C. Caratheodory, Untersuchungen ???ber die Grundlagen der Thermodynamik, Mathematische Annalen, vol.67, issue.3, pp.355-386, 1909.
DOI : 10.1007/BF01450409

E. Cartan, Sur l'intégration de certains systèmes indéterminés d'´ equations différentielles, J. für reine und angew. Math, vol.145, pp.86-91, 1915.

B. Charlet, J. Lévine, and R. Marino, On dynamic feedback linearization, Systems & Control Letters, vol.13, issue.2, pp.143-151, 1989.
DOI : 10.1016/0167-6911(89)90031-5

M. Fliess, A note on the invertibility of nonlinear input-output differential systems, Systems & Control Letters, vol.8, issue.2, pp.147-151, 1987.
DOI : 10.1016/0167-6911(86)90073-3

M. Fliess, J. Lévine, P. Martin, and P. Rouchon, ON DIFFERENTIALLY FLAT NONLINEAR SYSTEMS, Proc. IFAC-Symposium NOLCOS'92, 1992.
DOI : 10.1016/B978-0-08-041901-5.50031-2

M. Fliess, J. Lévine, P. Martin, and P. Rouchon, Sur les systèmes non linéaires différentiellement plats, Comptes Rendus, Académie des Sciences, 1992.

B. Gardner and W. F. Shadwick, The GS algorithm for exact linearization to Brunovsky normal form, IEEE Transactions on Automatic Control, vol.37, issue.2, pp.224-230, 1992.
DOI : 10.1109/9.121623

G. W. Haynes and H. Hermes, Nonlinear Controllability via Lie Theory, SIAM Journal on Control, vol.8, issue.4, pp.450-460, 1970.
DOI : 10.1137/0308033

]. D. Hilbert, ???ber den begriff der klasse von differentialgleichungen, Mathematische Annalen, vol.73, issue.1, pp.95-108, 1912.
DOI : 10.1007/BF01456663

B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Pol. Sci. Ser. Sci. Math, vol.28, pp.517-522, 1980.

R. M. Murray and S. S. Sastry, Nonholonomic motion planning: steering using sinusoids, IEEE Transactions on Automatic Control, vol.38, issue.5, 1991.
DOI : 10.1109/9.277235

URL : http://authors.library.caltech.edu/7315/1/MURieeetac93.pdf

R. M. Murray and S. S. Sastry, Steering nonholonomic systems in chained form, [1991] Proceedings of the 30th IEEE Conference on Decision and Control, pp.1121-1126, 1991.
DOI : 10.1109/CDC.1991.261508

S. N. Singh, A modified algorithm for invertibility in nonlinear systems, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.595-598, 1981.
DOI : 10.1109/TAC.1981.1102657

]. S. Bibliographie1 and . Asmi, Autour de l'inversion des systèmes entrée-sortie et du concept d'essentialité: une approche algébrique, 1992.

S. Asmi and M. Fliess, Formules d'inversion, Analysis of Controlled Dynamical Systems, pp.201-210, 1991.

M. D. Di-benedetto and J. H. Grizzle, Intrinsic notions of regularity for local inversion, output nulling, and dynamic extension of nonsquare systems, C-TAT, vol.6, issue.3, pp.357-381, 1990.

M. D. Di-benedetto, J. H. Grizzle, and C. H. Moog, Rank Invariants of Nonlinear Systems, SIAM Journal on Control and Optimization, vol.27, issue.3, pp.658-672, 1989.
DOI : 10.1137/0327035

R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior Differential Systems, 1991.
DOI : 10.1007/978-1-4613-9714-4

C. I. Byrnes and A. Isidori, Local stabilization of minimum-phase nonlinear systems, Systems & Control Letters, vol.11, issue.1, pp.9-17, 1988.
DOI : 10.1016/0167-6911(88)90105-3

E. Cartan, Lesprobì emes d'´ equivalence. Selecta, pp.113-136, 1937.

B. Charlet, J. Lévine, and R. Marino, On dynamic feedback linearization, Systems & Control Letters, vol.13, issue.2, pp.743-151, 1989.
DOI : 10.1016/0167-6911(89)90031-5

B. Charlet, J. Lévine, and R. Marino, Sufficient Conditions for Dynamic State Feedback Linearization, SIAM Journal on Control and Optimization, vol.29, issue.1, pp.38-57, 1991.
DOI : 10.1137/0329002

B. Novel, . Ph, R. Martin, and . Sépulchre, Full dynamic feedback linearization of a class of mechanical systems, Recent Advances in Mathematical Theory of Systems, Control, Network and Signal Processing II (MTNS 91, pp.327-333, 1992.

E. Delaleau and M. Fliess, AN ALGEBRAIC INTERPRETATION OF THE STRUCTURE ALGORITHM WITH AN APPLICATION TO FEEDBACK DECOUPLING, Proceedings of IFAC NOLCOS Conf, 1992.
DOI : 10.1016/B978-0-08-041901-5.50034-8

J. Descusse and C. H. Moog, Decoupling with dynamic compensation for strong invertible affine non-linear systems, International Journal of Control, vol.10, issue.1, pp.1387-1398, 1985.
DOI : 10.1080/00207178508933432

URL : https://hal.archives-ouvertes.fr/hal-00409989

J. Descusse and C. H. Moog, Dynamic decoupling for right-invertible nonlinear systems, Systems & Control Letters, vol.8, issue.4, pp.345-349, 1987.
DOI : 10.1016/0167-6911(87)90101-0

M. Fliess, A note on the invertibility of nonlinear input-output differential systems, Systems & Control Letters, vol.8, issue.2, pp.147-151, 1986.
DOI : 10.1016/0167-6911(86)90073-3

M. Fliess, Automatique et corps diff??rentiels, Forum Mathematicum, vol.1, issue.1, pp.227-238, 1989.
DOI : 10.1515/form.1989.1.227

M. Fliess, Generalized controller canonical form for linear and nonlinear dynamics, IEEE Transactions on Automatic Control, vol.35, issue.9, pp.994-1001, 1990.
DOI : 10.1109/9.58527

M. Fliess, J. Lévine, . Ph, P. Martin, and . Rouchon, On differentially flat non linear systems, Proceedings of IFAC NOLCOS Conf, 1992.

M. Fliess, J. Lévine, . Ph, P. Martin, and . Rouchon, Sur les systèmes nonlinéaires différentiellement plats, C.R. Acad. Sc. Paris, issue.I, pp.315619-624, 1992.

M. Fliess, J. Lévine, . Ph, P. Martin, and . Rouchon, Défaut d'un système non linéaire et commande haute fréquence, C.R. Acad. Sc. Paris, issue.I, p.316, 1993.

M. Fliess, J. Lévine, and P. Rouchon, Index of a general differential algebraic implicit system, Recent Advances in Mathematical Theory of Systems, Control, Network and Signal Processing II (MTNS 91, pp.289-294, 1992.

J. Hauser, S. Sastry, and G. Meyer, Nonlinear control design for slightly non-minimum phase systems: Application to V/STOL aircraft, Automatica, vol.28, issue.4, pp.665-679, 1992.
DOI : 10.1016/0005-1098(92)90029-F

]. D. Hilbert, ???ber den begriff der klasse von differentialgleichungen, Mathematische Annalen, vol.73, issue.1, pp.95-108, 1912.
DOI : 10.1007/BF01456663

H. J. Huijberts, Dynamic feedback in nonlinear synthesis problems, 1991.

H. J. Huijberts and H. Nijmeijer, STRONG DYNAMIC INPUT-OUTPUT DECOUPLING: FROM LINEARITY TO NONLINEARITY, Proceedings of IFAC NOLCOS Conf, 1992.
DOI : 10.1016/B978-0-08-041901-5.50033-6

L. R. Hunt, R. Su, and G. Meyer, Design for multi-input nonlinear systems, Differential Geometric Control Theory, pp.268-298, 1983.

A. Isidori, Nonlinear Control Systems, 1989.

B. Jakubczyk, Remarks on equivalence and linearization of non linear systems, Proceedings of IFAC NOLCOS Conf, 1992.

B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Pol. Sci., Ser. Sci. Math, vol.28, pp.9-10517, 1980.

P. Kokotovi´ckokotovi´c, H. K. Khalil, and J. O. Reilly, Singular perturbations methods in control: analysis and design, 1986.

E. R. Kolchin, Differential Algebra and Algebraic Groups, 1973.

R. Marino, On the largest feedback linearizable subsystem, Systems & Control Letters, vol.6, issue.5, pp.345-351, 1986.
DOI : 10.1016/0167-6911(86)90130-1

. Ph and . Martin, An intrinsic condition for regular decoupling, Systems & Control Letters, vol.20, 1993.

C. H. Moog, Nonlinear decoupling and structure at infinity, Mathematics of Control, Signals, and Systems, vol.35, issue.3, pp.275-268, 1988.
DOI : 10.1007/BF02551287

R. M. Murray and S. Sastry, Nonholonomic motion planning: steering using sinusoids, IEEE Transactions on Automatic Control, vol.38, issue.5, 1991.
DOI : 10.1109/9.277235

URL : http://authors.library.caltech.edu/7315/1/MURieeetac93.pdf

H. Nijmeijer, Right-invertibility for a class of nonlinear control systems: A geometric approach, Systems & Control Letters, vol.7, issue.2, pp.125-132, 1986.
DOI : 10.1016/0167-6911(86)90018-6

H. Nijmeijer and W. Respondek, Decoupling via dynamic compensation for nonlinear control systems, 1986 25th IEEE Conference on Decision and Control, pp.192-197, 1986.
DOI : 10.1109/CDC.1986.267206

J. F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, 1978.

W. Respondek, Intrinsic singularities of dynamic extensions Oral presentation, Proceedings of IFAC NOLCOS Conf, 1992.

W. Respondek and H. Nijmeijer, On local right-invertibility of nonlinear control systems, C-TAT, vol.4, issue.3, pp.325-328, 1988.

J. F. Ritt, Differential Algebra, 1950.
DOI : 10.1090/coll/033

S. N. Singh, A modified algorithm for invertibility in nonlinear systems, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.595-598, 1981.
DOI : 10.1109/TAC.1981.1102657

M. Vukobratovi´cvukobratovi´c and R. Stoji´cstoji´c, Modern Aircraft Flight Control, Ecole Nationale, vol.pilotage des avions, 1984.

E. T. Whittaker, A Treatise on the Analytical Dynamics of Particules and Rigid Bodies, 1937.

J. C. Willems, Paradigms and puzzles in the theory of dynamical systems, IEEE Transactions on Automatic Control, vol.36, issue.3, pp.259-294, 1991.
DOI : 10.1109/9.73561