R. Baer, Erweiterung von Gruppen und ihren Isomorphismen, Mathematische Zeitschrift, vol.160, issue.1, pp.375-416, 1934.
DOI : 10.1007/BF01170643

M. Barakat and D. Robertz, Computing invariants of multidimensional linear systems on an abstract homological level, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, 2006.

M. S. Boudellioua and A. Quadrat, Reduction of multidimensional linear systems: A moduletheoretic approach, 2007.

H. Cartan and S. Eilenberg, Homological Algebra, 1956.

F. Chyzak, A. Quadrat, and D. Robertz, Effective algorithms for parametrizing linear control systems over Ore algebras, Applicable Algebra in Engineering, Communication and Computing, vol.16, issue.5, pp.319-376, 2005.
DOI : 10.1007/s00200-005-0188-6

URL : https://hal.archives-ouvertes.fr/inria-00071407

F. Chyzak, A. Quadrat, and D. Robertz, OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems
DOI : 10.1007/978-3-540-49556-7_15

T. Cluzeau and A. Quadrat, Morphisms: A homological algebra package for factoring and decomposition linear functional systems, 2007.

T. Cluzeau and A. Quadrat, Factoring and decomposing a class of linear functional systems, Linear Algebra and its Applications, vol.428, issue.1, 2007.
DOI : 10.1016/j.laa.2007.07.008

URL : https://hal.archives-ouvertes.fr/hal-00320424

P. M. Cohn, Free Rings and Their Relations, 1985.

F. Dubois, N. Petit, and P. Rouchon, Motion planning and nonlinear simulations for a tank containing a fluid, Proc. of the 5th European Control Conf, 1999.

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 and H. Mounier, Controllability and observability of linear delay systems: an algebraic approach. ESAIM Control, Optimization and Calculus of Variations, pp.301-314, 1998.

T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, vol.189, 1999.
DOI : 10.1007/978-1-4612-0525-8

B. Malgrange, SystèmesSystèmesà coefficients constants, Séminaire Bourbaki, vol.246, pp.79-89

H. Mounier, J. Rudolph, M. Petitot, and M. Fliess, A flexible rod as a linear delay system, Proc. of the 3rd European Control Conference, 1995.

U. Oberst, Multidimensional constant linear systems, Acta Applicandae Mathematicae, vol.26, issue.124, pp.1-175, 1990.
DOI : 10.1007/BF00046908

N. Petit and P. Rouchon, Dynamics and solutions to some control problems for water-tank systems, IEEE Transactions on Automatic Control, vol.47, issue.4, pp.594-609, 2002.
DOI : 10.1109/9.995037

H. Pillai and S. Shankar, A Behavioral Approach to Control of Distributed Systems, SIAM Journal on Control and Optimization, vol.37, issue.2, pp.388-408, 1999.
DOI : 10.1137/S0363012997321784

J. W. Polderman and J. C. Willems, Introduction to Mathematical Systems Theory: A Behavioral Approach, Texts in Applied Mathematics, vol.26, 1998.
DOI : 10.1007/978-1-4757-2953-5

J. Pommaret, Partial Differential Control Theory, Mathematics and Its Applications . Kluwer, vol.530, 2001.
DOI : 10.1007/978-94-010-0854-9

J. Pommaret and A. Quadrat, Algebraic analysis of linear multidimensional control systems, IMA Journal of Mathematical Control and Information, vol.16, issue.3, pp.275-297, 1999.
DOI : 10.1093/imamci/16.3.275

J. Pommaret and A. Quadrat, A functorial approach to the behaviour of multidimensional control systems, Applied Mathematics and Computer Science, vol.13, pp.7-13, 2003.

A. Quadrat and D. Robertz, PARAMETRIZING ALL SOLUTIONS OF UNCONTROLLABLE MULTIDIMENSIONAL LINEAR SYSTEMS, 16 th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.00578

A. Quadrat and D. Robertz, On the Monge problem and multidimensional optimal control, 17 th International Symposium on Mathematical Theory of Networks and Systems, 2006.

J. J. Rotman, An Introduction to Homological Algebra, 1979.
DOI : 10.1007/b98977

J. Serre, Sur les modules projectifs Séminaire Dubreil-Pisot, pp.23-3461, 1960.
DOI : 10.1007/978-3-642-37726-6_48

URL : http://archive.numdam.org/article/SD_1960-1961__14_1_A2_0.pdf

S. Shankar, Synthesis of behaviours. In preparation, 2007.

J. Wood, Modules and behaviours in nD systems theory, Multidimensional Systems and Signal Processing, vol.11, issue.1/2, pp.11-48, 2000.
DOI : 10.1023/A:1008430528456

N. Yoneda, On Ext and exact sequences, J. Fac. Sci. Univ. Tokyo Sect. I, vol.8, p.507576, 1960.

. Unité-de-recherche-inria-sophia and . Antipolis, route des Lucioles -BP 93 -06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université -ZAC des Vignes 4, 2004.

I. Unité-de-recherche and . Lorraine, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt, Domaine de Voluceau -Rocquencourt -BP 105 -78153 Le Chesnay Cedex