Y. Aoustin, M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph, Theory and practice in the motion planning control of a flexible robot arm usingMikusì nski operators, Proc. of the Fifth IFAC Symposium on Robot Control, pp.287-293, 1997.

D. Brethébreth´brethé and J. J. Loiseau, A result that could bear fruit for the control of delay-differential systems, Proc. 4th IEEE Mediterranean Symp. Control Automation, pp.168-172, 1996.

D. Buchsbaum and D. Eisenbud, What makes a complex exact?, Journal of Algebra, vol.25, issue.2, pp.259-268, 1973.
DOI : 10.1016/0021-8693(73)90044-6

S. Y. Chung and J. Chung, There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable, Proceedings of the, pp.859-863, 2005.

R. F. Curtain and H. J. Zwart, An Introduction to Infinite- Dimensional Linear Systems Theory, 1995.
DOI : 10.1007/978-1-4612-4224-6

P. Destuynder, I. Legrain, L. Castel, and N. Richard, Theoretical , numerical and experimental discussion on the use of piezoelectric devices for control-structure interaction, Europ. J. Mecha. A/Solids, vol.11, pp.181-213, 1992.

C. De and . Boor, A pratical quide to spline, In Applied Mathematical Sciences, vol.27, 1978.

A. De-luca and A. B. Siciliano, Trajectory control of a non-linear one-link flexible arm, International Journal of Control, vol.49, issue.5, pp.1699-1715, 1989.
DOI : 10.1177/027836498800700404

V. Ditkine and A. Proudnikov, Transformations intégrales et calcul opérationnel, 1978.

D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, 1995.

A. El, A. J. Jai, and . Pritchard, Capteurs et actionneurs dans l'analyse des systèmes distribués, 1986.

A. Fabiaska and A. Quadrat, Applications of the Quillen-Suslin theorem to multidimensional systems theory, in Grbner Bases in Control Theory and Signal Processing, Radon Series on Computation and Applied Mathematics, de Gruyter publisher, pp.23-106, 2007.

N. Faiz, S. Agrawal, and R. Murray, Trajectory Planning of Differentially Flat Systems with Dynamics and Inequalities, Journal of Guidance, Control, and Dynamics, vol.24, issue.2, pp.219-227, 2001.
DOI : 10.2514/2.4732

T. Faulwasser, V. Hagenmeyer, and R. Findeisen, Optimal Exact Path-Following for Constrained Differentially Flat Systems, Proc. of 18th IFAC World Congress, pp.9875-9880, 2011.
DOI : 10.3182/20110828-6-IT-1002.03132

M. Fliess, Some basic structural properties of generalized linear systems, Systems & Control Letters, vol.15, issue.5, pp.391-396, 1990.
DOI : 10.1016/0167-6911(90)90062-Y

M. Fliess, J. L. Evine, P. Martin, and P. Rouchon, Flatness and defect of non-linear systems: introductory theory and applications, Internat. J. Control, pp.61-1327, 1995.

M. Fliess and H. Mounier, Quelques propriétés structurelles des systèmes linéaireslinéaires`linéairesà retards constants, C.R. Acad. Sci, pp.289-294, 1994.

M. Fliess and H. Mounier, Interpretation and comparison of various types of delay system controllabilities, Proc. IFAC Conf. System Struct. Control, pp.330-335, 1995.

M. Fliess and H. Mounier, Controllability and observability of linear delay systems: an algebraic approach, ESAIM: Control, Optimisation and Calculus of Variations, vol.3, p.301314, 1998.
DOI : 10.1051/cocv:1998111

M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph, Controllability and motion planning for linear delay systems with an application to a flexible rod, Proceedings of 1995 34th IEEE Conference on Decision and Control, pp.2046-2051, 1995.
DOI : 10.1109/CDC.1995.480649

H. Gl¨usinggl¨-gl¨using-l-¨ and . Uerssen, A Behavioral Approach To Delay-Differential Systems, SIAM Journal on Control and Optimization, vol.35, issue.2, pp.480-499, 1997.
DOI : 10.1137/S0363012995281869

I. M. Guelfand and G. E. Chilov, Generalized functions: fundamental spaces (translated from russian), 1968.

L. Hormander, The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients, 1990.
DOI : 10.1007/b138375

H. Komatsu and . Ultradistributions, Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.20, p.25105, 1973.

H. Komatsu, . Ultradistributions, and . Ii, The kernel theorem and ultradistributions with support in a manifold, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.24, pp.607-628, 1977.

V. Komornik, Exact Controllability and Stabilization, 1994.

J. E. Lagnese and J. ?. Lions, Modelling Analysis and Control of Thin Plates, 1988.

H. Laousy, C. Z. Xu, and G. Sallet, Boundary feedback stabilization of a rotating body-beam system, IEEE Transactions on Automatic Control, vol.41, issue.2, p.41, 1996.
DOI : 10.1109/9.481526

B. Laroche, P. Martin, and P. Rouchon, Motion planning for a class of partial differential equations with boundary control, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998.
DOI : 10.1109/CDC.1998.758247

E. K. Lavrossky, . Formal, and . Sky, On the stabilization of the angular position of an elastic rod, Technical Cyberneticss, vol.6, pp.115-123, 1989.

J. and ?. L. Lions, Contrôle optimal des systèmes gouvernés par deséquations des´deséquations aux dérivées partielles, 1968.

A. F. Lynch and J. Rudolph, Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems, International Journal of Control, vol.11, issue.15, pp.1219-1230, 2002.
DOI : 10.1524/auto.2000.48.8.399

O. Morg¨ulmorg¨ and . Morg¨ul, Dynamic boundary control of a Euler-Bernoulli beam, IEEE Transactions on Automatic Control, vol.37, issue.5, pp.639-652, 1992.
DOI : 10.1109/9.135504

O. Morg¨ulmorg¨ and . Morg¨ul, Control and stabilization of a rotating flexible structure, Automatica, vol.30, issue.2, pp.351-356, 1994.
DOI : 10.1016/0005-1098(94)90037-X

H. Mounier, Algebraic interpretations of the spectral controllability of a linear delay system, Proc. 3 rd Europ. Control Conf, pp.3325-3329, 1995.
DOI : 10.1515/form.10.1.39

H. Mounier, Propriétés structurelles des systèmes linéaireslinéaires`linéairesà retards : aspects théoriques et pratiques, Thèse, 1995.

H. Mounier, Algebraic interpretations of the spectral controllability of a linear delay system, Forum Mathematicum, vol.10, issue.1
DOI : 10.1515/form.10.1.39

H. Mounier, J. Rudolph, M. Petitot, and M. Fliess, A flexible rod as a linear delay system, Proc. 3 rd Europ. Control Conf, pp.3676-3681, 1995.

H. Mounier, J. Rudolph, and F. Woittennek, Boundary Value Problems and Convolutional Systems over Rings of Ultradistributions, of Contr., Sig. and Sys. with Physical Modeling Lect. Notes in Control and Information Sciences, vol.407, pp.179-188, 2010.
DOI : 10.1007/978-3-642-16135-3_15
URL : https://hal.archives-ouvertes.fr/hal-00526150

J. Oldenburg and W. Marquardt, Flatness and higher order differential model representations in dynamic optimization, Computers & Chemical Engineering, vol.26, issue.3, pp.385-400, 2002.
DOI : 10.1016/S0098-1354(01)00752-9

N. Petit, M. Milam, and R. Murray, Inversion based constrained trajectory optimization, Proc. of 5th IFAC symposium on nonlinear control systems, 2001.

A. Quadrat, An introduction to constructive algebraic analysis and its applications, les cours du CIRM, 1 no. 2: Journes Nationales de Calcul Formel, pp.281-471, 2010.

D. Quillen, Projective modules over polynomial rings, Inventiones Mathematicae, vol.61, issue.3, pp.167-171, 1976.
DOI : 10.1007/BF01390008

J. and ?. P. Ramis, Séries divergentes et théories asymptotiques, 1993.

L. Rodino, Linear Partial Differential Operators in Gevrey Spaces, 1993.
DOI : 10.1142/1550

J. Rotman, An Introduction to Homological Algebra, 2009.
DOI : 10.1007/b98977

J. Rudolph, Duality in Time-Varying Linear Systems: A Module Theoretic Approach, Linear Algebra Applications, to appear, 1996.

J. Rudolph and F. Woittennek, Motion planning and open loop control design for linear distributed parameter systems with lumped controls, International Journal of Control, vol.59, issue.3, pp.457-474, 2008.
DOI : 10.1051/cocv:2002070

P. Schapira, Microdifferential Systems in the Complex Domain, 1985.
DOI : 10.1007/978-3-642-61665-5

H. Sira-ram´irezram´irez and S. Agrawal, Differentially flat systems, Control Engineering Series, 2004.

A. A. Suslin, Projectives modules over a polynomial ring are free (in russian), Dokl. Akad. Nauk. SSSR Soviet. Math. Dokl, vol.229, issue.17, pp.1063-1066, 1976.

M. Tucsnak, Regularity and Exact Controllability for a Beam with Piezoelectric Actuator, SIAM Journal on Control and Optimization, vol.34, issue.3, pp.922-930, 1996.
DOI : 10.1137/S0363012994265468

F. Woittennek and H. Mounier, Controllability of Networks of Spatially One-Dimensional Second Order PDEs???An Algebraic Approach, SIAM Journal on Control and Optimization, vol.48, issue.6, pp.3882-3902, 2010.
DOI : 10.1137/08072437X

C. Z. Xu and J. Baillieul, Stabilizability and stabilization of a rotating body-beam system with torque control, IEEE Transactions on Automatic Control, vol.38, issue.12, pp.1754-1765, 1993.
DOI : 10.1109/9.250555