A. Bazet and V. Majd, An alternative way to test the criteria ensuring the existence of discrete-time normal form, Systems & control letters, vol.56, pp.4-315, 2007.

J. Barbot, I. Belmouhoub, and L. Boutat-baddas, Observability Quadratic Normal Forms In: New Trends in Nonlinear Dynamics & Control, & their Applications, LINCIS 295, pp.3-17, 2003.

J. Barbot, S. Monaco, and D. Normand-cyrot, Quadratic forms and approximate feedback linearization in discrete-time, Int. J.Control, issue.67 4, pp.567-586, 1997.

J. Barbot, S. Monaco, and D. , On the observer for differential /difference representations of discrete-time dynamics, European Control Conference, pp.5783-5788, 2007.

I. Belmouhoub, M. Djemai, and J. Barbot, An example of nonlinear discrete-time synchronization of chaotic systems for secure communication, European Cobtrol Conference- 2003, 2003.

I. Belmouhoub, M. Djemai, and J. Barbot, Cryptography by discrete-time hyperchaotic systems, 2003.

D. Boutat and J. Barbot, Poincaré Normal form for a class of driftless system in onedimensional submanifold neighborhood, Mathematics of Control Control, Signals and Systems, 2002.

L. Boutat-baddas, D. Boutat, J. Barbot, and R. Tauleigne, Quadratic observability normal form, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 2001.
DOI : 10.1109/CDC.2001.980723

L. Boutat-baddas, J. Barbot, D. Boutat, and R. Tauleigne, OBSERVABILITY BIFURCATION VERSUS OBSERVING BIFURCATIONS, Proc. IFAC. World Congress, 2002.
DOI : 10.3182/20020721-6-ES-1901.00248

P. Brunovsky, A classification of linear controllable systems, pp.173-188, 1970.

M. Fliess, S. Fuchshumer, M. Schöberl, K. Schlacher, and H. Sira-ramirez, An introduction to algebraic discrete-time linear parametric identification with a concrete application, Journal Europ??en des Syst??mes Automatis??s, vol.42, issue.2-3, pp.2-3, 2008.
DOI : 10.3166/jesa.42.211-232
URL : https://hal.archives-ouvertes.fr/inria-00188435

T. Floquet and J. Barbot, State and unknown input estimation for linear discrete-time systems, Automatica, vol.42, issue.11, pp.1883-1889, 2006.
DOI : 10.1016/j.automatica.2006.05.030
URL : https://hal.archives-ouvertes.fr/hal-00757977

F. Gordillo, F. Salas, R. Ortega, and J. , Hopf bifurcation in indirect field-oriented control of induction motors, Automatica, vol.38, issue.5, pp.829-835, 2002.
DOI : 10.1016/S0005-1098(01)00274-6

G. Gu, A. Sparks, and W. Kang, Biffurcation analysis and control for model via the projection method, Proc of, pp.3617-3621, 1998.

B. Hamzi, J. Barbot, S. Monaco, and D. Normand-cyrot, Nonlinear discrete-time control of systems with a Naimark???Sacker bifurcation, Systems & Control Letters, vol.44, issue.4, pp.245-258, 2001.
DOI : 10.1016/S0167-6911(01)00136-0

B. Hamzi, A. J. Krener, and W. Kang, The controlled center dynamics of discrete time control bifurcations, Systems & Control Letters, vol.55, issue.7, pp.585-596, 2006.
DOI : 10.1016/j.sysconle.2006.01.001

B. Hamzi and I. A. Tall, Normal forms for nonlinear discrete time control systems, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.9-12, 2003.
DOI : 10.1109/CDC.2003.1272798

H. J. Huijberts, T. Lilge, and H. Nijmeijer, NONLINEAR DISCRETE-TIME SYNCHRONIZATION VIA EXTENDED OBSERVERS, International Journal of Bifurcation and Chaos, vol.11, issue.07, pp.1997-2006, 2001.
DOI : 10.1142/S0218127401003218

H. J. Korsch and H. Jodl, Chaos, a program collection for the PC, 1999.

W. Kang, Bifurcation and Normal Form of Nonlinear Control Systems, Part II, SIAM Journal on Control and Optimization, vol.36, issue.1, pp.193-232, 1998.
DOI : 10.1137/S036301299529029X

W. Kang and A. J. Krener, Extended Quadratic Controller Normal Form and Dynamic State Feedback Linearization of Nonlinear Systems, SIAM Journal on Control and Optimization, vol.30, issue.6, pp.1319-1337, 1992.
DOI : 10.1137/0330070

A. J. Krener, Approximate linearization by state feedback and coordinate change, Systems & Control Letters, vol.5, issue.3, pp.181-185, 1984.
DOI : 10.1016/S0167-6911(84)80100-0

A. J. Krener, Feedback Linearization Mathematical Control Theory, pp.66-98, 1998.

T. Lilge, Nonlinear discrete-time observers for synchronization problems, nonlinear Observer Design, pp.491-510, 1999.
DOI : 10.1007/BFb0109941

S. Monaco and D. Normand-cyrot, The immersion under feedback of a multidimensional discrete-time nonlinear system into a linear one, International Journal of Control, pp.38-245, 1983.

S. Monaco and D. Normand-cyrot, Zero dynamics of sampled nonlinear systems, Systems & Control Letters, vol.11, issue.3, pp.229-234, 1988.
DOI : 10.1016/0167-6911(88)90063-1

S. Monaco and D. Normand-cyrot, Functional expansions for nonlinear discrete-time systems, Mathematical Systems Theory, vol.298, issue.1, pp.235-254, 1989.
DOI : 10.1007/BF02088015

S. Monaco and D. Normand-cyrot, Multirate three axes attitude stabilization of spacecraft, Proceedings of the 28th IEEE Conference on Decision and Control, 1989.
DOI : 10.1109/CDC.1989.70230

S. Monaco and D. Normand-cyrot, Normal forms and approximated feedback linearization in discrete time, Systems & Control Letters, vol.55, issue.1, pp.71-80, 2006.
DOI : 10.1016/j.sysconle.2005.04.016

S. Monaco and D. , Controller and observer normal forms in discretetime in Analysis and design of Nonlinear Control Systems, pp.377-396, 2008.

H. Nijmeijer and I. M. Mareels, An observer looks at synchronization. IEEE Trans. Circuits & Sys.-1: Fundamental Theory & Appli, pp.882-891, 1997.
DOI : 10.1109/81.633877
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.5342

W. Perruquetti and J. Barbot, Sliding mode control in engineering, Cont. Eng. Series. Marcel Dekker, 2002.
DOI : 10.1201/9780203910856

H. Poincaré, Les m??thodes nouvelles de la m??canique c??leste, Il Nuovo Cimento, vol.10, issue.1
DOI : 10.1007/BF02742713

A. Rapaport and A. Maloum, Embedding for exponential observers of nonlinear systems, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2000.
DOI : 10.1109/CDC.2000.912867

W. Respondek, Right and left invertibility of nonlinear control systems, pp.133-176, 1990.

M. K. Sain and J. L. Massey, Invertibility of linear time-invariant dynamical systems, IEEE Transactions on Automatic Control, vol.14, issue.2, pp.141-149, 1969.
DOI : 10.1109/TAC.1969.1099133