1. Articles:

    1. Quadrat, A. "Algebraic Analysis of Linear Functional Systems", book in preparation.

    2. Quadrat, A., Ushirobira, R. (2018). "On the Ore extension ring of differential time-varying delay operators", submitted for publication.

    3. Quadrat, A., Regensburger, G. (2018). "Computing polynomial solutions and annihilators of integro-differential operators with polynomial coefficients", INRIA Research Report n. 9002 ( paper.pdf ), to appear in the book Algebraic Methods and Symbolic-Numeric Computation in Systems Theory, Advances in Delays and Dynamics (ADD), volume 9, Springer.

    4. Cluzeau, T., Quadrat, A. (2018). "Equivalences of linear functional systems", INRIA Research Report n. 9000 ( paper.pdf ), to appear in the book Algebraic Methods and Symbolic-Numeric Computation in Systems Theory, Advances in Delays and Dynamics (ADD), volume 9, Springer.

    5. Cluzeau, T., Koutschan, C., Quadrat, A., Tõnso, M. (2018). "Effective algebraic analysis approach to linear systems over Ore algebras", INRIA Research Report n. 8999 ( paper.pdf ), to appear in the book Algebraic Methods and Symbolic-Numeric Computation in Systems Theory, Advances in Delays and Dynamics (ADD), volume 9, Springer.

    6. Quadrat, A. (2016), Appendix of Pommaret, J.-F., "Bianchi identities for the Riemann and Weyl tensors" ( paper.pdf ), arXiv:1603.05030 , 16/04/2016. Also in the book Pommaret, J.-F., Deformation Theory of Algebraic and Geometric Structures, Lambert Academic Publishing, 2016.

    7. Cluzeau, T., Quadrat, A. (2015). "A new insight into Serre's reduction problem", INRIA Research Report n. 8629 ( paper.pdf ), Linear Algebra and its Applications, vol. 483, pp. 40-100.

    8. Quadrat, A., Robertz, D. (2014). "A constructive study of the module structure of rings of partial differential operators", INRIA Research Report n. 8225 ( paper.pdf ), Acta Applicandæ Mathematicæ, vol. 133, pp. 187-234.

    9. Quadrat, A., (2013). "Grade filtration of linear functional systems", INRIA Research Report n. 7769 ( paper.pdf ), Acta Applicandæ Mathematicæ, vol. 127, pp. 27-86.

    10. Cluzeau, T., Dolean, V., Nataf, F., Quadrat, A. (2013). "Symbolic techniques for domain decomposition methods", in Domain Decomposition Methods in Science and Engineering XX, R. Bank et al. (Eds.), Lecture Notes in Computational Science and Engineering (LNCSE), vol. 91, Springer, pp. 27-38, extracted from "Symbolic methods for developing new domain decomposition algorithms", INRIA Research Report n. 7953 ( paper.pdf ).

    11. Cluzeau, T., Quadrat, A. (2012). "Serre's reduction of linear systems of partial differential equations with holonomic adjoints", Journal of Symbolic Computation, vol. 47, pp. 1192-1213, INRIA Research Report n. 7486 ( paper.pdf ).

    12. Boudellioua, M. S., Quadrat, A., (2010). "Serre's reduction of linear functional systems", INRIA Research Report n. 7214 , Mathematics in Computer Science, vol. 4, pp. 289-312 ( paper.pdf ).

    13. Quadrat, A., (2010). "An introduction to constructive algebraic analysis and its applications", les cours du CIRM, 1 no. 2: Journées Nationales de Calcul Formel (2010), pp. 281-471, INRIA Research Report n. 7354 ( paper.pdf ).

    14. Cluzeau, T., Quadrat, A. (2009). "OreMorphisms: A homological algebraic package for factoring, reducing and decomposing linear functional systems", in Topics in Time-Delay Systems: Analysis, Algorithms and Control, J.-J. Loiseau, W. Michiels, S.-I. Niculescu, R. Sipahi (Eds.), Lecture Notes in Control and Information Sciences (LNCIS), vol. 388, Springer, pp. 179-196 ( paper.pdf ).

    15. Cluzeau, T., Quadrat, A. (2009). "On algebraic simplifications of linear functional systems", in Topics in Time-Delay Systems: Analysis, Algorithms and Control, J.-J. Loiseau, W. Michiels, S.-I. Niculescu, R. Sipahi (Eds.), Lecture Notes in Control and Information Sciences (LNCIS), vol. 388, Springer, pp. 167-178 ( paper.pdf ).

    16. Cluzeau, T., Quadrat, A. (2008). "Factoring and decomposing a class of linear functional systems", INRIA Research Report n. 5942 , Linear Algebra and Its Applications, vol. 428, pp. 324-381 ( paper.pdf ).

    17. Quadrat, A., Robertz, D. (2007). "On the Baer extension problem for multidimensional linear systems", INRIA Research Report n. 6307 ( paper.pdf ).

    18. Quadrat, A., Robertz, D. (2007). "Computation of bases of free modules over the Weyl algebras", INRIA Research Report n. 5786 , Journal of Symbolic Computation, vol. 42, pp. 1113-1141 ( paper.pdf ).

    19. Fabiańska, A., Quadrat, A. (2007). "Applications of the Quillen-Suslin theorem to multidimensional systems theory", INRIA Research Report n. 6126 , in Gröbner Bases in Control Theory and Signal Processing, H. Park, G. Regensburger (Eds.), Radon Series on Computation and Applied Mathematics 3, de Gruyter publisher, pp. 23-106 ( paper.pdf ).

    20. Chyzak, F., Quadrat, A., Robertz, D. (2007). "OreModules: A symbolic package for the study of multidimensional linear systems", in Applications of Time-Delay Systems, J. Chiasson, J.-J. Loiseau, (Eds.), Lecture Notes in Control and Information Sciences (LNCIS), vol. 352, Springer, pp. 233-264 ( paper.pdf ).

    21. Chyzak, F., Quadrat, A., Robertz, D. (2005). "Effective algorithms for parametrizing linear control systems over Ore algebras", INRIA Research Report n. 5181 , Applicable Algebra in Engineering, Communications and Computing, vol. 16, n. 5, pp. 319-376 ( paper.pdf ).

    22. Pommaret, J.-F., Quadrat, A. (2004). "A differential operator approach to multidimensional optimal control", International Journal of Control, vol. 77, pp. 821-836 ( paper.pdf ).

    23. Pommaret, J.-F., Quadrat, A. (2003). "A functorial approach to the behaviour of multidimensional control systems", Applied Mathematics and Computer Science, vol. 13, pp. 7-13 ( paper.pdf ).

    24. Pommaret, J.-F., Quadrat, A. (2000). "Formal elimination for multidimensional systems and applications to control theory", Mathematics of Control, Signal and Systems, vol. 13, pp. 193-215 ( paper.pdf ).

    25. Pommaret, J.-F., Quadrat, A. (1999). "Algebraic analysis of linear multidimensional control systems", IMA J. Mathematical Control & Information, vol. 16, pp. 275-297 ( paper.pdf ).

    26. Pommaret, J.-F., Quadrat, A. (1999). "Localization and parametrization of linear multidimensional systems", Systems & Control Letters, vol. 37, pp. 247-260 ( paper.pdf ).

    27. Pommaret, J.-F., Quadrat, A. (1998). "Generalized Bezout Identity", Applicable Algebra in Engineering, Communications and Computing, vol. 9, pp. 91-116 ( paper.pdf ).

  2. Congress papers:

    1. Boulier, F., Castel, H., Corson, N., Lanza, N., Lemaire, L., Poteaux, A., Quadrat, A., Verdière, N. (2018). "Symbolic-numeric methods for nonlinear integro-differential modeling", to appear in the proceedings of Computer Algebra in Scientific Computing 2018, Lille (France), 17-21/08/2018.

    2. Cluzeau, T., Hossein, J., Quadrat, A., Raab C., Regensburger, G. (2018). "Symbolic computation for integro-differential-time-delay operators with matrix coefficients", proceedings of 14th IFAC Workshop on Time Delay Systems , Budapest (Hungary), 28-30/06/2018.

    3. Cluzeau, T., Hossein, J., Quadrat, A., Raab, C., Regensburger, G. (2017). "Symbolic computation for operators with matrix coefficients", poster at Foundations of Computational Mathematics (FoCM 2017), Barcelona (Spain), 10-19/07/2017 ( poster.pdf ).

    4. Quadrat, A., (2017). "Towards an effective study of the algebraic parameter estimation problem", hal-01415300, Proceedings of IFAC 2017 Workshop Congress , Toulouse (France), 09-14/07/2017 ( paper.pdf ).

    5. Ushirobira, R., Quadrat, A., (2016). "Algebraic estimation of a biased and noisy continuous signal via orthogonal polynomials", Proceedings of 55th IEEE Conference on Decision and Control, Las Vegas (USA), 12-14/12/2016 ( paper.pdf ).

    6. Quadrat, A., Ushirobira, R. (2016). "Algebraic analysis for the Ore extension rings of differential time-varying delay operators", in the proceedings of 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS) , University of Minnesota, Minneapolis (USA), 12-15/07/2016 ( paper.pdf ).

    7. Bekcheva, M., Greco, L., Mounier, H., Quadrat, A. (2015). "Euler-Bernoulli beam flatness based control with constraints", Proceedings of the IEEE 9th International Workshop on Multidimensional (nD) Systems (IEEE nDS 2015), Vila Real (Portugal) (07-09/09/15) ( paper.pdf ).

    8. Quadrat, A. (2015). "A constructive algebraic analysis approach to Artstein's reduction of linear time-delay systems", Proceedings of 12th IFAC Workshop on Time Delay Systems , University of Michigan, Ann Arbor (USA), 28-30/05/2015 ( paper.pdf ).

    9. Quadrat, A. (2014). "Study of a spectral sequence central in the behavioural approach", Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen (The Netherlands), 07-11/07/2014 ( paper.pdf ).

    10. Quadrat, A. (2014). "Restrictions of n-D behaviours and inverse images of D-modules", Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen (The Netherlands), 07-11/07/2014 ( paper.pdf ).

    11. Cluzeau, T., Quadrat, A. (2013). "Isomorphisms and Serre's reduction of linear systems", Proceedings of nDS13, Erlangen (Germany) (9-11/09/13) ( paper.pdf ).

    12. Quadrat, A. (2013). "Yoneda product of multidimensional systems", Proceedings of nDS13, Erlangen (Germany) (9-11/09/13) ( paper.pdf ).

    13. Quadrat, A., Regensburger, G. (2013). "Polynomial solutions and annihilators of ordinary integro-differential operators", Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France), (04-06/02/13) ( paper.pdf ).

    14. Quadrat, A., Robertz, D. (2013). "Stafford's reduction of linear partial differential systems", Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France), (04-06/02/13) ( paper.pdf ).

    15. Cluzeau, T., Quadrat, A. (2013). "Further results on the decomposition and Serre's reduction of linear functional systems", Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France), (04-06/02/13) ( paper.pdf ).

    16. Cluzeau, T., Dolean, V., Nataf, F., Quadrat, A. (2011). "Symbolic preconditioning techniques for linear systems of partial differential equations", Proceedings of 20th International Conference on Domain Decomposition Methods (DD20), UC San Diego (USA) (07-11/02/11) ( paper.pdf )

    17. Quadrat, A. (2011). "Purity filtration of multidimensional linear systems", Proceedings of nDS'11, Poitiers (France) (05-07/09/11) ( paper.pdf ).

    18. Quadrat, A. (2011). "Equidimensional triangularization of multidimensional linear systems", Proceedings of nDS'11, Poitiers (France) (05-07/09/11) ( paper.pdf ).

    19. Cluzeau, T., Quadrat, A. (2011). "A constructive version of Fitting's theorem on isomorphisms and equivalences of linear systems", Proceedings of nDS'11, Poitiers (France) (05-07/09/11) ( paper.pdf ).

    20. Chakhar, A., Cluzeau, T., Quadrat, A. (2011). "An algebraic analysis approach to certain classes of nonlinear partial differential systems", Proceedings of nDS'11, Poitiers (France) (05-07/09/11) ( paper.pdf ).

    21. Barkatou, M., El Bacha, C., Cluzeau, T., Quadrat, A. (2011). "Monge parametrizations and integration of rectangular linear differential systems", MEGA 2011, Stockholm (Sweden) (30/05-03/06/11).

    22. Quadrat, A. (2010). "Purity filtration of 2-dimensional linear systems", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10), also in Algebraic Systems Theory, Behaviors, and Codes, E. Zerz (Eds.), Shaker, 2010, 15-22 ( paper.pdf ).

    23. Boudellioua, M. S., Quadrat, A. (2010). "Further results on Serre's reduction of multidimensional linear systems", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10) ( paper.pdf ).

    24. Cluzeau, T., Quadrat, A. (2010). "Serre's reduction of linear partial differential systems based on holonomy", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10) ( paper.pdf ).

    25. Cluzeau, T., Quadrat, A. (2010). "Symmetries, parametrizations and potentials of multidimensional linear systems", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10), also in Algebraic Systems Theory, Behaviors, and Codes, E. Zerz (Eds.), Shaker, 2010, 7-14 ( paper.pdf ).

    26. Cluzeau, T., Quadrat, A. (2010). "Module structure of classical multidimensional linear systems appearing in mathematical physics", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10) ( paper.pdf ).

    27. Quadrat, A., Robertz, D. (2010). "Controllability and differential flatness of linear analytic ordinary differential systems", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10), also in Algebraic Systems Theory, Behaviors, and Codes, E. Zerz (Eds.), Shaker, 2010, 23-30 ( paper.pdf ).

    28. Quadrat, A. (2010). "Extendability of multidimensional linear systems", Proceedings of MTNS 2010, Budapest (Hungary) (05-07/07/10).

    29. Quadrat, A. (2009). "A normal form for 2-dimensional linear systems", ACA 2009, Montreal (Quebec) (25-28/06/09).

    30. Quadrat, A. (2008). "New perspectives in algebraic systems theory", semi-plenary session MTNS 2008, Blacksburg, Virginia (USA) (28/07-01/08/08) ( Abstract.pdf , paper.pdf , slides.pdf ).

    31. Boudellioua, M. S., Quadrat, A. (2008). "Reduction of linear systems based on Serre's theorem", Proceedings of MTNS 2008, Blacksburg, Virginia (USA) (28/07-01/08/08) ( paper.pdf ).

    32. Quadrat, A., Robertz, D. (2008). "Baer's extension problem for multidimensional linear systems", Proceedings of MTNS 2008, Blacksburg, Virginia (USA) (28/07-01/08/08) ( paper.pdf ).

    33. Cluzeau, T., Quadrat, A. (2006). "Using morphism computations for factoring and decomposing general linear functional systems", Proceedings of MTNS 2006, Kyoto (Japan) (24-28/07/06) ( paper.pdf ).

    34. Fabiańska, A., Quadrat, A. (2006). "Flat multidimensional linear systems with constant coefficients are equivalent to controllable 1-D linear systems", Proceedings of MTNS 2006, Kyoto (Japan) (24-28/07/06) ( paper.pdf ).

    35. Quadrat, A., Robertz, D. (2006). "Constructive computation of flat outputs of a class of multidimensional linear systems with variable coefficients", Proceedings of MTNS 2006, Kyoto (Japan) (24-28/07/06) ( papier.pdf ).

    36. Quadrat, A., Robertz, D. (2006). "On the Monge problem and multidimensional optimal control", Proceedings of MTNS 2006, Kyoto (Japan) (24-28/07/06) ( paper.pdf ).

    37. Quadrat, A., Robertz, D. (2005). "On the blowing-up of stably free behaviours", Proceedings of CDC-ECC05, Seville (Spain) (12-15/12/05) ( paper.pdf ).

    38. Quadrat, A., Robertz, D. (2005). "Parametrizing all solutions of uncontrollable multidimensional linear systems", Proceedings of 16th IFAC World Congress, Prague (Czech Republic) (04-08/07/05) ( paper.pdf ).

    39. Chyzak, F., Quadrat, A., Robertz, D. (2004). "OreModules: A symbolic package for the study of multidimensional linear systems", Proceedings of MTNS 2004, Leuven (Belgium) (05-09/07/04) ( paper.pdf ).

    40. Chyzak, F., Quadrat, A., Robertz, D. (2003). "Linear control systems over Ore algebras. Effective algorithms for the computation of parametrizations", Proceedings of the Workshop on Time-Delay Systems (TDS03), IFAC Workshop, INRIA Rocquencourt (France) (08-10/09/03) ( paper.pdf ).

    41. Quadrat, A. (2001). "Extended Bézout identities", Proceedings of ECC, Porto (Portugal) ( paper.pdf ).

    42. Pommaret, J.-F., Quadrat, A. (2000). "Equivalences of linear control systems", Proceedings of MTNS 2000, Perpignan (France) ( paper.pdf ).

    43. Pommaret, J.-F., Quadrat, A. (2000). "A functorial approach to the behaviour of multidimensional control systems", Proceedings of International Workshop on Multidimensional Systems (NDS), Czocha Castle (Poland), pp. 91-96 ( paper.pdf ).

    44. Pommaret, J.-F., Quadrat, A. (1997). "Formal obstructions to the controllability of partial differential control systems", Proceedings of IMACS, Berlin (Germany), vol. 5, pp. 209-214 ( paper.pdf ).

  3. Others:

    1. Barakat, M., Coquand, T., Quadrat, A. (2013). Oberwolfach Mini-Workshop "Constructive homological algebra with applications to coherent sheaves and control theory", Oberwolfach, 12-18/05/13 ( report.pdf ).

    2. Coquand, T., Quadrat, A., Yengui, I. (2009). Oberwolfach Mini-Workshop "Formal methods in commutative algebra: A view toward constructive homological algebra", Oberwolfach, 08-14/11/09 ( report.pdf ).

    3. Quadrat, A. (2007). "Une introduction aux théories algébriques différentielles", Intéractions entre théories algébriques et calcul scientifiquence: Etat-de-l'art et applications (CNAM 18/09/07) ( slides.pdf ).

    4. Quadrat, A. (2007). "Introduction à quelques résultats récents d'automatique linéaire basés sur des méthodes de calcul formel", Journées Doctorales-Journées Nationales du GdR MACS, Reims (France) (09-11/07/07) ( slides.pdf ).

    5. Quadrat, A. (2006). "Factorization and and decomposition of linear functional systems", Lectures IRCCyN Nantes (France) (28-30/11/06) and at Aachen University (Germany) (11-22/12/06), Journées nationales de calcul formel (CIRM) (29/01-02/02/07) ( slides.pdf ).

    6. Quadrat, A. (2006). "Using effective homological algebra for factoring and decomposing linear functional systems", Special Semester on Grobner Bases and Related Methods 2006 (D2) , RISC-Linz (Austria) (15/05/06), ALGO Seminar , INRIA Rocquencourt (France) (26/05/06) ( slides.pdf ).

    7. Quadrat, A. (2005). "Constructive computation of bases over the Weyl algebras", Aachen University (Germany), (27/09/05), Journées nationales de calcul formel CIRM (21-25/11/05), Innsbruck University (Austria) (07/12/05), Linz-RISC University (Austria) (12/12/05), Special Semester on Grobner Bases and Related Methods 2006 (D3) , RISC-Linz (Austria) (19/05/06) ( slides.pdf ).

    8. Quadrat, A. (2005). "On the Monge problem for multidimensional linear systems", CAFE Seminar Day, INRIA Sophia Antipolis (30/08/05) ( slides.pdf ).

    9. Quadrat, A. (2005). "An algebraic analysis approach to mathematical system theory", NETCA Workshop: Verification and Theorem Proving for Continuous Systems, Oxford (United Kingdom) (26/08/05) ( slides.pdf , OreModules.pdf , Annex.pdf ).

    10. Quadrat, A. (2005). "Contributions de Charles Méray à l'étude des systèmes d'équations aux dérivées partielles", Colloque en hommage à Charles Méray, Mathématicien et Vigneron Chalonnais (1835-1911), Chalon sur Saône (France) (09/06/05) ( slides.pdf ).

    11. Quadrat, A. (2005). "An introduction to constructive algebraic analysis", WorkShop Mathematics, Algorithms, Proofs, Schloss Dagstuhl (Germany) (09-14/01/05).

    12. Quadrat, A. (2004). "Introduction to symbolic methods for differential time-delay control systems", 2nd WorkShop CNRS-NSF, Applications of Time-Delay Systems, Nantes (France) (13-15/09/04) ( slides.pdf ).

    13. Quadrat, A. (2003). "Etude de la platitude des systèmes linéaires différentiels à retards: Algorithmes & Implantation", Journées Nationales d'Automatique (JNA) (25-27/06/03), Valenciennes (France).

    14. Quadrat, A. (2003). "Parametrizations of underdetermined linear systems of partial differential equations: Algorithms and Applications", Journées nationales de calcul formel CIRM (20-24/01/03).

    15. Quadrat, A. (2002). "Calcul effectif des paramétrisations des systèmes à retards", Working group GT "Systèmes à retards'' (GdR Automatique) (13/06/02).

    16. Quadrat, A. (2002). "An introduction to algebraic analysis with effective applications to linear control systems", Lectures at the University of Aachen (Germany) (03-07/06).

    17. Quadrat, A. (2002). "Systems of partial differential equations: an introduction to the works of D. C. Spencer and his school", Lecture Notes of the working group Involution.

    18. Quadrat, A. (2002). "Systems of partial differential equations: an introduction to the works of C. Riquier and M. Janet", Lecture Notes of the working group Involution.

    19. Nihtilä, M. T., Tervo, J., Quadrat, A. (2001). "Algebraic approach to the controllability of boundary-value systems", SIAM conference on Linear Algebra in Signals, Systems and Control, Boston (USA) (13-16/07/01).

    20. Quadrat, A. (2000). "Analyse algébrique pour l'automatique linéaire", ALGO Seminar , INRIA Rocquencourt (France) (04/12/00) ( slides.ps.gz ).

    21. Quadrat, A. (1999). "Analyse algébrique des systèmes de contrôle linéaires multidimensionnels", PhD thesis, École Nationale des Ponts et Chaussées (France) (23/09/99).

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