M. Amidou and I. Yengui, An algorithm for unimodular completion over Laurent polynomial rings, Linear Algebra and its Applications, vol.429, issue.7, 2006.
DOI : 10.1016/j.laa.2008.05.002

J. E. Bjork, Rings of Differential Operators, 1979.

Y. A. Blinkov, C. F. Cid, V. P. Gerdt, W. Plesken, and D. Robertz, The MAPLE Package Janet " : I. Polynomial Systems Also available with the package from http, the Proccedings of Computer Algebra in Scientific Computing CASC 2003, pp.31-40

F. Chyzak, A. Quadrat, and D. Robertz, OreModules project, directly available from http

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 " , in the book Applications of Time-Delay Systems, LNCIS 352, 2007.

R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts in Applied Mathematics, vol.21, 1991.
DOI : 10.1007/978-1-4612-4224-6

T. Cluzeau and A. Quadrat, Using morphism computations for factoring and decomposition general linear functional systems, pp.20-24

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

D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, vol.150, 1994.

J. Evers, Implementation of the Quillen-Suslin theorem in OreModules, 2005.

A. Fabia´nskafabia´nska, QuillenSuslin project: A package for computing bases of free modules over commutative polynomial rings

A. Fabia´nskafabia´nska and A. Quadrat, Flat multidimensional linear systems with constant coefficients are equivalent to controllable 1-D linear systems, pp.24-2806, 2006.

N. Fitchas and A. Galligo, Nullstellensatz effectif et Conjecture de Serre (Th??or??me de Quillen-Suslin) pour le Calcul Formel, Mathematische Nachrichten, vol.51, issue.1, pp.149-231, 1990.
DOI : 10.1002/mana.19901490118

M. Fliess, J. Lévine, P. Martin, and P. Rouchon, Flatness and defect of nonlinear systems: introductory theory and examples, Int. J. Control, pp.61-1327, 1995.

M. Fliess, J. Lévine, P. Martin, and P. Rouchon, A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems, IEEE Trans. Automatic Control, pp.40-922, 1999.

M. Fliess and H. Mounier, Controllability and observability of linear delay systems: an algebraic approach, ESAIM: Control, Optimisation and Calculus of Variations, pp.301-314, 1998.
DOI : 10.1051/cocv:1998111

J. Gago-vargas, Constructions in R[x 1 , . . . , x n ]: applications to K-theory, Journal of Pure and Applied Algebra, pp.171-185, 2002.

G. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, 2002.
DOI : 10.1007/978-3-662-04963-1

M. Kashiwara, Algebraic Study of Systems of Partial Differential Equations, Master's Thesis, 1970.

R. C. Laubenbacher and C. J. Woodburn, A new algorithm for the Quillen-Suslin Theorem, Contributions to Algebra and Geometrie, pp.41-64, 2000.

T. Y. Lam, Serre's Conjecture, Lecture Notes in Mathematics, vol.635, 1978.
DOI : 10.1007/BFb0068340

T. Y. Lam, Serre's Problem on projective Modules, 2006.
DOI : 10.1007/978-3-540-34575-6

Z. Lin and N. K. Bose, A generalization of Serre's conjecture and some related issues, Linear Algebra and its Applications, vol.338, issue.1-3, pp.125-138, 2001.
DOI : 10.1016/S0024-3795(01)00370-6

A. Logar and B. Sturmfels, Algorithms for the Quillen-Suslin theorem, Journal of Algebra, vol.145, issue.1, pp.231-239, 1992.
DOI : 10.1016/0021-8693(92)90189-S

H. Logemann, On the transfer matrix of a neutral system: Characterizations of exponential stability in input???output terms, Systems & Control Letters, vol.9, issue.5, pp.393-400, 1987.
DOI : 10.1016/0167-6911(87)90068-5

H. Lombardi and I. Yengui, Suslin???s algorithms for reduction of unimodular rows, Journal of Symbolic Computation, vol.39, issue.6, pp.707-717, 2005.
DOI : 10.1016/j.jsc.2005.01.004

B. Malgrange, SystèmesSystèmes`Systèmesà coefficients constants, Séminaire Bourbaki, vol.63, pp.1-11, 1962.

G. Monge, Supplément o` u l'on fait voir que leséquationsleséquations aux différences ordinaires pour lesquelles les conditions d'intégrabilité ne sont pas satisfaites sont susceptibles d'une véritable intégration, Mémoire Académie des Sciences, vol.1784, pp.502-576

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

H. Mounier, J. Rudolph, M. Fliess, and P. Rouchon, Tracking control of a vibrating string with an interior mass viewed as delay system, ESAIM: Control, Optimisation and Calculus of Variations, vol.3, p.315321, 1998.
DOI : 10.1051/cocv:1998112

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

V. P. Palamodov, Linear Differential Operators with Constant Coefficients, 1970.
DOI : 10.1007/978-3-642-46219-1

H. Park, A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems, 1995.

H. Park and C. Woodburn, An Algorithmic Proof of Suslin???s Stability Theorem for Polynomial Rings, Journal of Algebra, vol.178, issue.1, pp.277-298, 1995.
DOI : 10.1006/jabr.1995.1349

H. Park, Symbolic computation and signal processing, Journal of Symbolic Computation, vol.37, issue.2, pp.209-226, 2004.
DOI : 10.1016/j.jsc.2002.06.003

H. Park, Generalizations and variations of Quillen-Suslin theorem and their applications " , workshop Gröbner Bases in Control Theory and Signal Processing, Special semester on Gröbner bases and related methods, p.6, 2006.

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.47-595, 2002.
DOI : 10.1109/9.995037

H. K. 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, Solving Bose conjecture on linear multidimensional systems, Proceedings of European Control Conference (ECC), pp.4-0701

J. Pommaret and A. Quadrat, Generalized Bezout Identity, Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.2, pp.91-116, 1998.
DOI : 10.1007/s002000050096
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.9863

J. Pommaret and A. Quadrat, Localization and parametrization of linear multidimensional control systems, Systems & Control Letters, vol.37, issue.4, pp.247-260, 1999.
DOI : 10.1016/S0167-6911(99)00030-4

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, Equivalences of linear control systems, proceedings 14 th International Symposium on Mathematical Theory of Networks and Systems (MTNS2000), pp.19-2300

J. Pommaret and A. Quadrat, A differential operator approach to multidimensional optimal control, International Journal of Control, vol.75, issue.9, pp.77-821, 2004.
DOI : 10.1007/BF02741885

A. Quadrat, Extended Bézout identities, proceedings of the European Control Conference (ECC), pp.4-07

A. Quadrat, The fractional representation approach to synthesis problems: an algebraic analysis viewpoint. Part I: (weakly) doubly coprime factorizations, Part II: internal stabilization, SIAM J. Control & Optimization, pp.42-266, 2003.

A. Quadrat, On a generalization of the Youla???Ku??era parametrization. Part I: the fractional ideal approach to SISO systems, Systems & Control Letters, vol.50, issue.2, pp.50-135, 2003.
DOI : 10.1016/S0167-6911(03)00149-X

A. Quadrat, A lattice approach to analysis and synthesis problems, Mathematics of Control, Signals, and Systems, vol.18, issue.2, pp.147-186, 2006.
DOI : 10.1007/s00498-005-0159-2

A. Quadrat and D. Robertz, Constructive computation of bases of free modules over the Weyl algebras submitted for publication, www-sop.inria.fr/apics/personnel/Alban, INRIA Report, vol.5786, 2005.

]. A. Quadrat and D. Robertz, The Stafford project " , directly available from wwwb.math.rwth-aachen

A. Quadrat and D. Robertz, Constructive computation of flat outputs of multidimensional linear systems, pp.20-2406

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

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

A. A. Suslin, Projective modules over polynomial rings are free, Dokl. Akad. Nauk. S.S.S.RSoviet Math. Dokl, vol.229, issue.17, pp.1160-1164, 1976.

L. N. Vaser?tein and A. A. Suslin, SERRE'S PROBLEM ON PROJECTIVE MODULES OVER POLYNOMIAL RINGS, AND ALGEBRAIC $ K$-THEORY, Mathematics of the USSR-Izvestiya, vol.10, issue.5, pp.937-1001, 1976.
DOI : 10.1070/IM1976v010n05ABEH001822

M. Vidyasagar, Control System Synthesis: A Factorization Approach, Part I, Synthesis Lectures on Control and Mechatronics, vol.2, issue.1, 1985.
DOI : 10.2200/S00351ED1V01Y201105CRM002

I. Yengui, Suslin's lemma for elimination, 2006.

D. C. Youla and P. F. , The Quillen - Suslin theorem and the structure of n-dimensional elementary polynomial matrices, IEEE Transactions on Circuits and Systems, vol.31, issue.6, pp.31-513, 1984.
DOI : 10.1109/TCS.1984.1085545

M. Wang and D. Feng, On Lin???Bose problem, Linear Algebra and its Applications, vol.390, pp.279-285, 2004.
DOI : 10.1016/j.laa.2004.04.020

M. Wang and C. P. Kwong, On multivariate polynomial matrix factorizations problems, Math. Control Signals Systems, vol.17, pp.297-311, 2005.

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

E. Zerz, Topics in Multidimensional Linear Systems Theory, Lecture Notes in Control and Information Sciences, vol.256, 2000.

P. Zervos, Leprobì eme de Monge, Mémorial des sciences mathématiques, fasicule LIII, 1932.

I. 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