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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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GAIA - 2018


Major publications by the team in recent years
  • 1F. Boulier, C. Chen, F. Lemaire, M. Moreno-Maza.

    Real root isolation of regular chains, in: Computer Mathematics, 2014, pp. 33–38.
  • 2F. Boulier, F. Lemaire, J. Lallemand, G. Regensburger, M. Rosenkranz.

    Additive normal forms and integration of differential fractions, in: Journal of Symbolic Computation, 2016, vol. 77, pp. 16–38.
  • 3F. Boulier, F. Lemaire, M. Rosenkranz, R. Ushirobira, N. Verdière.

    On symbolic approaches to integro-differential equations, Springer, 2019, pp. 165–184.
  • 4Y. Bouzidi, S. Lazard, G. Moroz, M. Pouget, F. Rouillier.

    Separating linear forms and rational univariate representations of bivariate systems, in: Journal of Symbolic Computation, 2015, vol. 68, pp. 84–119.
  • 5Y. Bouzidi, A. Poteaux, A. Quadrat.

    A symbolic computation approach towards the asymptotic stability analysis of differential systems with commensurate delays, in: Delays and Interconnections: Methodology, Algorithms and Applications, Advances in Delays and Dynamics (ADD), Springer, 2018.
  • 6Y. Bouzidi, A. Quadrat, F. Rouillier.

    Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems, in: Multidimensional Systems and Signal Processing, June 2018.
  • 7F. Chyzak, A. Quadrat, D. Robertz.

    Effective algorithms for parametrizing linear control systems over Ore algebras, in: Applicable Algebra in Engineering, Communications and Computing, 2005, vol. 16, pp. 319–376.
  • 8T. Cluzeau, A. Quadrat.

    Factoring and decomposing a class of linear functional systems, in: Linear Algebra and Its Applications, 2008, vol. 428, pp. 324–381.
  • 9A. Poteaux, M. Rybowicz.

    Good reduction of Puiseux series and applications, in: Journal of Symbolic Computation, 2012, vol. 47, pp. 32–63.
  • 10A. Poteaux, M. Rybowicz.

    Improving complexity bounds for the computation of Puiseux series over finite fields, in: ISSAC, 2015, pp. 299–306.
  • 11A. Quadrat, A. Quadrat.

    Delay effects in visual tracking problems for an optronic sighting system, in: Low-Complexity Controllers for Time-Delay Systems, Advances in Delays and Dynamics (ADD), Springer, 2014, vol. 2, pp. 77–92.
  • 12G. Rance, Y. Bouzidi, A. Quadrat, A. Quadrat.

    H parametric control via algebraic Riccati equations, in: 22nd International Symposium on Mathematical Theory of Networks and Systems (MTNS, 2016.
  • 13R. Ushirobira, W. Perruquetti, M. Mboup.

    An algebraic continuous time parameter estimation for a sum of sinusoidal waveform signals, in: International Journal of Adaptive Control and Signal Processing, 2016, vol. 30, pp. 1689–1713.
  • 14R. Ushirobira, A. Quadrat.

    Algebraic estimation of a biased and noisy continuous signal via orthogonal polynomials, in: 55th IEEE Conference on Decision and Control (CDC), 2016.
Publications of the year

Doctoral Dissertations and Habilitation Theses

Articles in International Peer-Reviewed Journals

  • 16H. Ahmed, R. Ushirobira, D. Efimov.

    Robust global synchronization of Brockett oscillators, in: IEEE Transactions on Control of Network Systems, 2018, pp. 1-10. [ DOI : 10.1109/tcns.2018.2813927 ]
  • 17F. Boulier, F. Lemaire, A. Poteaux, M. Moreno Maza.

    An Equivalence Theorem For Regular Differential Chains, in: Journal of Symbolic Computation, 2018, pp. 1-27.
  • 18Y. M. Bouzidi, A. Quadrat, F. Rouillier.

    Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems, in: Multidimensional Systems and Signal Processing, June 2018.
  • 19X. Deru, F. Lemaire, D. Nicolas.

    From Etaples to Pompei. Discussion about Metal Vessel in Roman Household, in: Herom, 2018, Définition d’un modèle à partir des données écrites et archéologiques du camp napoléonien d’Etaples, confrontation des données céramologiques romaines en Gaule et en Italie.
  • 20D. Efimov, R. Ushirobira, J. A. Moreno, W. Perruquetti.

    Homogeneous Lyapunov functions: from converse design to numerical implementation, in: SIAM Journal on Control and Optimization, December 2018.
  • 21J. G. Rueda-Escobedo, R. Ushirobira, D. Efimov, J. Moreno.

    Gramian-based uniform convergent observer for stable LTV systems with delayed measurements, in: International Journal of Control, 2018.
  • 22H. Silm, R. Ushirobira, D. Efimov, J.-P. Richard, W. Michiels.

    A note on distributed finite-time observers, in: IEEE Transactions on Automatic Control, May 2018. [ DOI : 10.1109/TAC.2018.2838042 ]

International Conferences with Proceedings

  • 23A. Barrau, G. Rance, Y. Bouzidi, A. Quadrat, A. Quadrat.

    Using symbolic computation to solve algebraic Riccati equations arising in invariant filtering, in: ECC2018 - European Control Conference, Limassol, Cyprus, June 2018.
  • 24P.-A. Bliman, D. Efimov, R. Ushirobira.

    A class of nonlinear adaptive observers for SIR epidemic model, in: ECC 2018 - European Control Conference, Limassol, Cyprus, June 2018, 6 p.
  • 25M. Nancel, S. Aranovskiy, R. Ushirobira, D. Efimov, S. Poulmane, N. Roussel, G. Casiez.

    Next-Point Prediction for Direct Touch Using Finite-Time Derivative Estimation, in: Proceedings of the ACM Symposium on User Interface Software and Technology (UIST 2018), Berlin, Germany, October 2018. [ DOI : 10.1145/3242587.3242646 ]
  • 26J. G. Rueda-Escobedo, R. Ushirobira, D. Efimov, J. Moreno.

    A Gramian-based observer with uniform convergence rate for delayed measurements, in: ECC 2018 - 16th annual European Control Conference, Limassol, Cyprus, June 2018.
  • 27H. Silm, R. Ushirobira, D. Efimov, W. Michiels, J.-P. Richard, E. Fridman.

    Comparison of the Time-Delay Margin of a Distributed and Centralized Observer, in: ECC 2018 - European Control Conference, Limassol, Cyprus, June 2018.

Conferences without Proceedings

  • 28F. Boulier.

    On the Parameter Estimation Problem for Integro-Differential Models, in: AADIOS @ ACA 2018, Santiago de Compostela, Spain, June 2018.
  • 29F. Boulier, H. Castel, N. Corson, V. Lanza, F. Lemaire, A. Poteaux, A. Quadrat, N. Verdière.

    Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling, in: CASC 2018 - The 20th International Workshop on Computer Algebra in Scientific Computing, Lille, France, September 2018.

Other Publications

  • 30F. Boulier.

    The Management of Parameters in the MAPLE DifferentialAlgebra Package, June 2018, working paper or preprint.
  • 31F. Boulier, F. Fages, O. Radulescu, S. S. Samal, A. Schuppert, W. M. Seiler, T. Sturm, S. Walcher, A. Weber.

    The SYMBIONT Project: Symbolic Methods for Biological Networks, August 2018, F1000Research 7:1341 (poster).
  • 32G. Perozzi.

    Optimization of the control effort for quadrotors using a varying-gain quasi-continuous sliding mode control influenced by a wind estimator, April 2018, working paper or preprint.
References in notes
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    Hamiltonian Systems and Their Integrability, American Mathematical Society, 2008.
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  • 38J.-D. Bauch, E. Nart, H. Stainsby.

    Complexity of the OM factorizations of polynomials over local fields, in: LMS Journal of Computation and Mathematics, 2013, vol. 16, pp. 139–171.
  • 39V. V. Bavula.

    The algebra of integro-differential operators on an affine line and its modules, in: J. Pure Appl. Algebra, 2013, vol. 217, pp. 495–529.
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  • 42N. K. Bose.

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  • 43N. K. Bose.

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  • 46F. Boulier, D. Lazard, F. Ollivier, M. Petitot.

    Computing representations for radicals of finitely generated differential ideals, in: Appl. Algebra Engrg. Comm. Comput., 2009, vol. 20, pp. 73–121.
  • 47Y. Bouzidi, T. Cluzeau, G. Moroz, A. Quadrat.

    Computing effectively stabilizing controllers for a class of nD systems, in: Proc. of the 20th World Congress of the International Federation of Automatic Control (IFAC'17), 9-14 July 2017, 2017.
  • 48Y. Bouzidi, A. Quadrat, F. Rouillier.

    Computer algebra methods for testing the structural stability of multidimensional systems, in: IEEE 9th International Workshop on Multidimensional Systems (NDS), 2015.
  • 49D. Bridges, R. Mines, F. Richman, P. Schuster.

    The polydisk Nullstellensatz, in: Proceedings of the American Mathematical Society, 2003, vol. 132, pp. 2133–2140.
  • 50B. Buchberger.

    Gröbner bases: An algorithmic method in polynomial ideal theory, in: Multidimensional Systems Theory: Progress, Directions and Open Problems in Multidimensional Systems, N. K. Bose (editor), Reidel, 1985, pp. 184–232.
  • 51E. Cartan.

    Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, 1971.
  • 52X. Caruso, D. Roe, T. Vaccon.

    Division and slope factorization of p-adic polynomials, in: International Symposium on Symbolic and Algebraic Computation (ISSAC), 2016.
  • 53A. Connes.

    Noncommutative Geometry, Academic Press, 1994.
  • 54R. F. Curtain, H. J. Zwart.

    An Introduction to Infinite-Dimensional Linear Systems Theory, Springer, 1995.
  • 55R. Dagher, A. Quadrat, G. Zheng.

    Auto-localisation par mesure de distances, Pattern FR1853553, Inria France, 2018.
  • 56R. Dagher, A. Quadrat, G. Zheng.

    Algebraic solutions to the metric multidimensional unfolding. Application to the position self-calibration problem, in: Pattern under development, 2017.
  • 57L. Denis–Vidal, G. Joly–Blanchard, C. Noiret.

    System identifiability (symbolic computation) and parameter estimation, in: Numerical Algorithms, 2003, vol. 34, pp. 282–-292.
  • 58S. Diop.

    Elimination in control theory, in: Math. Control Signals Systems, 1991, vol. 4, pp. 17–32.
  • 59S. Diop.

    Differential-algebraic decision methods and some applications to system theory, in: Theoret. Comput. Sci., 1992, vol. 98, pp. 137–161.
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    Cortical spreading ischaemia is a novel process involved in ischaemic damage in patients with aneurysmal subarachnoid haemorrhage, in: Brain, 2009, vol. 132, pp. 1866–1881.
  • 61D. Duval.

    Rational Puiseux expansions, in: Compositio Mathematica, 1989, vol. 70, pp. 119–154.
  • 62A. Fabiańska, A. Quadrat.

    Applications of the Quillen-Suslin theorem to multidimensional systems theory, in: Gröbner Bases in Control Theory and Signal Processing, Radon Series on Computation and Applied Mathematics, d. Gruyter (editor), H. Park, G. Regensburger, 2007, vol. 3, pp. 23–106,
  • 63M. Fliess, S. T. Glad.

    An algebraic approach to linear and nonlinear control, in: Essays on Control: Perspectives in the Theory and its Applications, Birkhaüser (editor), 1993, pp. 223–267.
  • 64M. Fliess, H. Mounier.

    Controllability and observability of linear delay systems: an algebraic approach, in: ESAIM Control Optim. Calc. Var., 1998, vol. 3, pp. 301–314.
  • 65M. Fliess, H. Sira-Ramírez.

    An algebraic framework for linear identification, in: ESAIM Control Optim. Calc. Variat., 2003, vol. 9, pp. 151–168.
  • 66H. Gluesing-Luerssen.

    Linear Delay-Differential Systems with Commensurate Delays: An Algebraic Approach, Lecture Notes in Mathematics, Springer, 1995, vol. 1770.
  • 67M. Gromov.

    Partial Differential Relations, Springer, 1986.
  • 68J. Guàrdia, J. Montes, E. Nart.

    Newton polygons of higher order in algebraic number theory, in: Transactions of the American Mathematical Society, 2012, vol. 364, pp. 361–416.
  • 69E. Hairer, G. Wanner.

    Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, Springer, 2010, vol. 14.
  • 70J. K. Hale, S. M. V. Lunel.

    Introduction to Functional Differential Equations, Applied Mathematical Sciences, Springer, 1993, vol. 99.
  • 71E. Hubert, A. Barrau, M. E. Badaoui.

    New multi-carrier demodulation method applied to gearbox vibration analysis, in: 2018 IEEE International Conference on Acoustics, Speech, and Signal, Calgary, 15-20/04/2018, 2018.
  • 72E. Hubert.

    Notes on triangular sets and triangulation-decomposition algorithms II: Differential Systems, in: Symbolic and Numerical Scientific Computations, LNCS, Springer (editor), Springer, 2003, vol. 2630, pp. 40–87.
  • 73T. Kailath.

    Linear Systems, Prentice-Hall, 1980.
  • 74F. Kako, T. Sasaki.

    Solving multivariate algebraic equations by Hensel construction, in: Japan J. of Industrial and Applied Math., 1999, vol. 16, pp. 257–285.
  • 75M. Kashiwara.

    Algebraic Study of Systems of Partial Differential Equation, Mémoires de la Société Mathématiques de France, 1995, vol. 63, Transl. from Japanese of his 1970 Master's Thesis.
  • 76E. R. Kolchin.

    Differential Algebra and Algebraic Groups, Academic Press, 1973.
  • 77T. Y. Lam.

    Serre's Problem on Projective Modules, Monograph in Mathematics, Springer, 2006.
  • 78J. J. Loiseau.

    Algebraic tools for the control and stabilization of time-delay systems, in: IFAC Reviews, Annual Reviews in Control, 2000, vol. 24, pp. 135–149.
  • 79J. C. McConnell, J. C. Robson.

    Noncommutative Noetherian Rings, American Mathematical Society, 2000..
  • 80U. Oberst.

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  • 81P. Olver.

    Applications of Lie Groups to Differential Equations, Springer, 1993.
  • 82A. Parisa, A. Masoud, M. M. Maza.

    On the extended Hensel construction and its application to the computation of limit points, in: International Symposium on Symbolic and Algebraic Computation (ISSAC), 2017.
  • 83J. W. Polderman, J. C. Willems.

    Introduction to Mathematical Systems Theory. A Behavioral Approach, TAM, Springer, 1998, vol. 26.
  • 84J.-F. Pommaret.

    Partial Differential Control Theory. Volume II: Control Systems, Kluwer, 2001.
  • 85J.-F. Pommaret.

    Systems of Partial Differential Equations and Lie Pseudogroups, Gordon and Breach, 1978.
  • 86J.-F. Pommaret.

    Partial Differential Equations and Group Theory: New Perspectives for Applications, Kluwer, 1994.
  • 87A. Poteaux.

    Calcul de développements de Puiseux et application au calcul du groupe de monodrmie d'une courbe algébrique plane, University of Limoges, 2008.
  • 88A. Poteaux, M. Weimann.

    A dichotomic Newton-Puiseux algorithm using dynamic evaluation, in: Preprint available at, 2017.
  • 89A. Quadrat.

    The fractional representation approach to synthesis problems: an algebraic analysis viewpoint. Part I: (weakly) doubly coprime factorizations, Part II: internal stabilization, in: SIAM J. Control & Optimization, 2003, vol. 42, pp. 266–299, 300–320.
  • 90A. Quadrat.

    A lattice approach to analysis and synthesis problems. On a generalization of the Youla-Kucˇera parametrization. Part II: The lattice approach to MIMO systems, in: Mathematics of Control, Signals, and Systems, 2006, vol. 18, pp. 147–186, 199–235.
  • 91A. Quadrat.

    An introduction to constructive algebraic analysis and its applications, in: Les cours du CIRM, Journées Nationales de Calcul Formel, CIRM, 2010, vol. 1, pp. 281–471.
  • 92A. Quadrat.

    Noncommutative geometric structures on stabilizable infinite-dimensional linear systems, in: European Control Conference, Strasbourg (France), 2014.
  • 93A. Quadrat.

    A constructive algebraic analysis approach to Artstein's reduction of linear time-delay systems, in: Proceedings of 12th IFAC Workshop on Time Delay Systems (TDS), 2015.
  • 94A. Quadrat.

    Towards an effective study of the algebraic parameter estimation problem, in: Proceedings of 20th World Congress of the International Federation of Automatic Control (IFAC'17), 2017.
  • 95A. Quadrat, G. Regensburger.

    Computing polynomial solutions and annihilators of integro-differential operators with polynomial coefficients, in: Algebraic and Symbolic Computation Methods in Dynamical Systems, Springer, 2018, vol. 9, pp. 87–111.
  • 96A. Quadrat, D. Robertz.

    Computation of bases of free modules over the Weyl algebras, in: Journal of Symbolic Computation, 2007, vol. 42, pp. 1113–1141.
  • 97A. Quadrat, D. Robertz.

    A constructive study of the module structure of rings of partial differential operators, in: Acta Applicandæ Mathematicæ, 2014, vol. 133, pp. 187–243.
  • 98G. Rance, Y. Bouzidi, A. Quadrat, A. Quadrat.

    Explicit H controllers for 1st to 3rd order single-input single-output systems with parameters, in: Proceedings of IFAC 2017 Workshop Congress, 2017.
  • 99G. Rance, Y. Bouzidi, A. Quadrat, A. Quadrat.

    Parametric sub-optimal H controllers for an optro-mechanical system modeled by a time-delay 4th order system, in: 8th International Symposium on Optronics in Defence and Security, OPTRO2018, accepted, 2018.
  • 100G. Rance, Y. Bouzidi, A. Quadrat, A. Quadrat, F. Rouillier.

    Explicit H controllers for 4th order single-input single-output systems with parameters and their applications to the two mass-spring system with damping, in: Proceedings of IFAC 2017 Workshop Congress, 2017.
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  • 106T. Sánchez, J. A. Moreno.

    A constructive Lyapunov function design method for a class of homogeneous systems, in: 53rd IEEE Conference on Decision and Control, Los Angeles, 2014, pp. 5500–5505.
  • 107T. Sánchez, J. A. Moreno.

    An SOS method for the design of continuous and discontinuous differentiators, in: International Journal of Control, 2017, vol., pp. 1–18.
  • 108R. Ushirobira, A. Quadrat.

    Algebraic estimation of a biased and noisy continuous signal via orthogonal polynomials, in: 55th IEEE Conference on Decision and Control, 2016.
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    Galois Theory of Linear Differential Equations, Springer, 2002.