Team apics

Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities


Major publications by the team in recent years

D. Avanessoff, J.-B. Pomet.
Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states, in: ESAIM Control Optim. Calc. Var., 2007, vol. 13, no 2, p. 237-264
L. Baratchart, A. Ben Abda, F. Ben Hassen, J. Leblond.
Recovery of pointwise sources or small inclusions in 2D domains and rational approximation, in: Inverse Problems, 2005, no 21, p. 51–74.
L. Baratchart, J. Grimm, J. Leblond, J. R. Partington.
Approximation and interpolation in H2 : Toeplitz operators, recovery problems and error bounds, in: Integral Equations and Operator Theory, 2003, vol. 45, p. 269–299.
L. Baratchart, R. Kuestner, V. Totik.
Zero distributions via orthogonality, in: Annales de l'Institut Fourier, 2005, vol. 55, no 5, p. 1455-1499.
L. Baratchart, J. Leblond, J.-P. Marmorat.
Sources identification in 3D balls using meromorphic approximation in 2D disks, in: Electronic Transactions on Numerical Analysis (ETNA), 2006, vol. 25, p. 41–53.
L. Baratchart, F. Mandréa, E. B. Saff, F. Wielonsky.
2D inverse problems for the Laplacian: a meromorphic approximation approach, in: Journal de Math. Pures et Appliquées, 2008, vol. 86, p. 1-41.
L. Baratchart, M. Olivi.
Critical points and error rank in best H2 matrix rational approximation of fixed McMillan degree, in: Constructive Approximation, 1998, vol. 14, p. 273-300.
L. Baratchart, E. B. Saff, F. Wielonsky.
A criterion for uniqueness of a critical point in H2 rational approximation, in: Journal d'Analyse, 1996, vol. 70, p. 225-266.
L. Baratchart, F. Seyfert.
An Lp analog to AAK theory for p$ \ge$2 , in: Journal of Functional Analysis, 2002, vol. 191, no 1, p. 52–122.
B. Hanzon, M. Olivi, R. Peeters.
Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm, in: Linear Algebra and its Applications, 2006, vol. 418, p. 793-820.
J.-P. Marmorat, M. Olivi.
Nudelman Interpolation, Parametrization of Lossless Functions and balanced realizations, in: Automatica, 2007, vol. 43, no 1329–1338.

Publications of the year

Doctoral Dissertations and Habilitation Theses

J.-B. Pomet.
Equivalence et linéarisation des systèmes de contrôle, Université de Nice - Sophia Antipolis, October 2009, Habilitation à Diriger des Recherches (HDR).

Articles in International Peer-Reviewed Journal

B. Atfeh, L. Baratchart, J. Leblond, J. R. Partington.
Bounded extremal and Cauchy–Laplace problems on the sphere and shell, in: J. of Fourier Analysis and Applications, 2009
L. Baratchart, F. L. Nazarov, V. V. Peller.
Analytic approximation of matrix functions in Lp , in: Journal of Approximation Theory, 2009, vol. 158, p. 242-278.
L. Baratchart, J.-B. Pomet.
On local linearization of control systems, in: J. of Dynamical and Control Systems, 2009, vol. 15, no 4, p. 471-536
L. Baratchart, M. Yattselev.
Convergent interpolation to Cauchy integrals, in: Foundations of Computational Mathematics, 2009, vol. 9, no 6, p. 675-715.
L. Baratchart, M. Yattselev.
Meromorphic approximants to complex Cauchy transforms with polar singularities, in: Mat. Sbornik, 2009, vol. 200, no 9, p. 3-40.
L. Baratchart, M. Yattselev.
Multipoint Padé approximants to complex Cauchy transforms with polar singularities, in: Journal of Approximation Theory, 2009, vol. 156, p. 187-211.
M. Bekheit, S. Amari, F. Seyfert.
A New Approach to Canonical Dual-Mode Cavity Filter Design, in: IEEE Transactions on Microwave Theory and Techniques, 2009, vol. 57, p. 1196-1206.
A. Ben Abda, F. Ben Hassen, J. Leblond, M. Mahjoub.
Sources recovery from boundary data: a model related to electroencephalography, in: Mathematical and Computer Modelling, 2009, vol. 49, p. 2213-2223
A. Figalli, L. Rifford.
Mass Transportation on sub-Riemannian Manifolds, in: Geom. Funct. Anal., 2010, to appear.
J. Grimm.
Convertir du LaTeX en HTML passant par XML :Deux exemples d'utilisation de Tralics, in: Cahiers Gutenberg, 2009, no 51, p. 25-55, octobre 2008, to appear.
M. Jaoua, J. Leblond, M. Mahjoub, J. R. Partington.
Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains, in: IMA J. of Applied Mathematics, 2009, vol. 74, p. 481-506
J.-B. Pomet.
A necessary condition for dynamic equivalence, in: SIAM J. on Control and Optimization, 2009, vol. 48, p. 925-940
M. Yattselev.
On the multiplicity of singular values of Hankel operators whose symbol is a Cauchy transform on a segment, in: Journal of Operator Theory, 2009, vol. 61, no 2, p. 239-251.

International Peer-Reviewed Conference/Proceedings

L. Baratchart, M. Yattselev.
Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in L2 of the Circle, in: International Workshop on Orthogonal Polynomials and Approximation Theory, P. Marcellan Eds., Contemporary Mathematics, (USA), 2009, to appear.
B. Hanzon, M. Olivi, R. Peeters.
Subdiagonal pivot structures and associated caninical forms under state isometry, in: Sysid, St-Malo, France, 2009.
R. Peeters, M. Olivi, B. Hanzon.
Balanced realizations of lossless systems : Schur parameters, canonical forms and applications, in: Sysid, St-Malo, France, 2009.

Internal Reports

L. Baratchart, J. Leblond, F. Seyfert.
Extremal problems of mixed type in H2 of the circle, INRIA, 2009, no RR-7087, Rapport de recherche.
J. Grimm.
Implementation of Bourbaki's Elements of Mathematics in Coq: Part One, Theory of Sets, INRIA, 2009, no RR-6999, Research Report.
J. Grimm.
Implementation of Bourbaki's Elements of Mathematics in Coq: Part Two; Ordered Sets, Cardinals, Integers, INRIA, 2009, no RR-7150, Research Report.

References in notes

A. Agrachev, P. Lee.
Optimal transportation under nonholonomic constraints, in: Trans. Amer. Math. Soc., 2009, vol. 361, no 11, p. 6019–6047
D. Alpay, L. Baratchart, A. Gombani.
On the Differential Structure of Matrix-Valued Rational Inner Functions, in: Operator Theory : Advances and Applications, 1994, vol. 73, p. 30-66.
S. Amari.
Application of representation theory to dual-mode microwave bandpass filter synthesis, in: IEEE Trans. Microwave Theory and Technique, 2010, to appear.
L. Ambrosio, S. Rigot.
Optimal mass transportation in the Heisenberg group, in: J. Funct. Anal., 2004, vol. 208, no 2, p. 261–301
Z. Artstein.
Stabilization with relaxed control, in: Nonlinear Analysis TMA, 1983, vol. 7, p. 1163-1173.
D. Avanessoff.
Linéarisation dynamique des systèmes non linéaires et paramétrage de l'ensemble des solutions, Univ. de Nice - Sophia Antipolis, June 2005, Ph. D. Thesis.
D. Avanessoff, L. Baratchart, J.-B. Pomet.
Sur l'intégrabilité (très) formelle d'une partie des équations de la platitude des systèmes de contrôle, INRIA, December 2003, no 5045, Rapport de recherche.
L. Baratchart.
On the H2 Rational Approximation of Markov Matrix-Valued Functions, in: Proc. 17th Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japon, 2006, p. 180-182.
L. Baratchart, M. Cardelli, M. Olivi.
Identification and rational L2 approximation: a gradient algorithm, in: Automatica, 1991, vol. 27, p. 413-418.
L. Baratchart, M. Chyba, J.-B. Pomet.
A Grobman-Hartman theorem for control systems, in: J. of Dynamics and Differential Equations, 2007, vol. 19, no 1, p. 75–107
L. Baratchart, P. Enqvist, A. Gombani, M. Olivi.
Minimal symmetric Darlington synthesis, in: Math. of Control, Signal & Syst, 2007, vol. 4, p. 283-311.
L. Baratchart, J. Leblond.
Hardy approximation to Lp functions on subsets of the circle with 1$ \le$p<$ \infty$ , in: Constructive Approximation, 1998, vol. 14, p. 41-56.
L. Baratchart, J. Leblond, F. Mandréa, E. B. Saff.
How can meromorphic approximation help to solve some 2D inverse problems for the Laplacian?, in: Inverse Problems, 1999, vol. 15, p. 79–90.
L. Baratchart, J. Leblond, J. R. Partington.
Hardy approximation to Im13 $L^\#8734 $ functions on subsets of the circle, in: Constructive Approximation, 1996, vol. 12, p. 423-435.
L. Baratchart, J. Leblond, S. Rigat, E. Russ.
Hardy spaces of the conjugate Beltrami equation, submited for publication.
L. Baratchart, J. Leblond, F. Seyfert.
Extremal problems of mixed type in H2 of the circle, in preparation.
L. Baratchart, M. Olivi.
Index of critical points in l2 -approximation, in: System and Control Letters, 1988, vol. 10, p. 167–174.
L. Baratchart, H. Stahl, F. Wielonsky.
Asymptotic uniqueness of best rational approximants of given degree to Markov functions in L2 of the circle, in: Constr. Approx., 2001, vol. 17, no 1, p. 103–138.
L. Baratchart, M. Yattselev.
Convergent interpolation to Cauchy integrals over analytic arcs with Jacobi type weights, submitted for publication.
S. Bila, D. Baillargeat, M. Aubourg, S. Verdeyme, P. Guillon, F. Seyfert, J. Grimm, L. Baratchart, C. Zanchi, J. Sombrin.
Direct Electromagnetic Optimization of Microwave Filters, in: IEEE Microwave Magazine, 2001, vol. 1, p. 46-51.
S. Bila, R. Cameron, P. Lenoir, V. Lunot, F. Seyfert.
Chebyshev Synthesis for Multi-Band Microwave Filter, in: Microwave Symposium Digest, IEEE MTT-S International, June 2006, p. 1221 - 1224
J. Blum.
Numerical simulation and optimal control in plasma physics, with applications to Tokamaks, Wiley/Gauthier-Villars, 1989.
A. Bombrun.
Les Transferts Orbitaux à Faible Poussée : Optimalité et Feedback, École des Mines de Paris, March 2007, Ph. D. Thesis.
A. Bombrun, J.-B. Pomet.
The average control system, under preparation.
A. Bombrun, J.-B. Pomet.
On the Average Control System, in: 17th Int. Sympos. on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto, Japan, July 2006, p. 2912-2917.
A. Bombrun, J.-B. Pomet.
Asymptotic behavior of the time optimal orbital transfer for low thrust 2-body control system, in: DCDS supplements, September 2007, vol. 2007, p. 122-129
N. Bourbaki.
Elements of Mathematics, Theory of Sets, Springer, 1968.
Y. Brenier.
Polar factorization and monotone rearrangement of vector-valued functions, in: Comm. Pure Appl. Math., 1991, vol. 44, no 4, p. 375–417
A. Bultheel, P. González-Vera, E. Hendriksen, O. Njåstad.
Orthogonal rational functions, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 1999, vol. 5.
J.-B. Caillau, J. Gergaud, J. Noailles.
Minimum time control of the Kepler equation, in: Unsolved problems in mathematical systems and control theory, V. D. Blondel, A. Megretski (editors), Princeton University Press, 2004.
S. Chaabane, I. Fellah, M. Jaoua, J. Leblond.
Logarithmic stability estimates for a Robin coefficient in 2D Laplace inverse problems, in: Inverse Problems, 2004, vol. 20, no 1, p. 49–57.
M. Clerc, J. Leblond, J.-P. Marmorat, T. Papadopoulo, M. Zghal.
Sources localization in EEG using rational approximation on plane sections, in preparation.
Y. Fischer, J. Leblond.
Solutions conjugate Beltrami equations and approximation in generalized Hardy spaces, submited for publication.
Y. Fischer, J. Leblond, J. R. Partington, E. Sincich.
Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply connected domains, submited for publication.
M. Fliess, J. Lévine, P. Martin, P. Rouchon.
Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples, in: Int. J. of Control, 1995, vol. 61, p. 1327–1361.
P. Fulcheri, M. Olivi.
Matrix rational H2 -approximation: a gradient algorithm based on Schur analysis, in: SIAM J. on Control & Optim., 1998, vol. 36, p. 2103-2127.
J. B. Garnett.
Bounded analytic functions, Academic Press, 1981.
J. Grimm.
Converting LaTeX to MathML: the Tralics algorithms, INRIA, 2007, no 6373, Research Report.
J. Grimm.
Producing MathML with Tralics, INRIA, 2007, no RR-6181, Research Report.
J. Grimm.
Tralics, a LaTeX to XML translator, Part II, INRIA, 2007, no RT-0310, Research Report.
J. Grimm.
Tralics, a LaTeX to XML translator; Part I, INRIA, 2008, no RT-0309, Rapport Technique.
T. Iwaniec, G. Martin.
Geometric function theory and non-linear analysis, Oxford Univ. Press, 2001.
L. V. Kantorovich.
On a problem of Monge, in: Uspekhi mat. Nauka, 1948, vol. 3, p. 225–226, reprinted in J. Math. Sci. (N. Y.) 133 (2006), 1383–1383.
J. Karel, S. Haddad, R. Westra, W. Serdijn, R. Peeters.
Implementing wavelets in continuous-time analog circuits with dynamic range optimization, in: IEEE Trans. on circuits and systems, 2009.
S. Khrushchev.
Schur's algorithm, orthogonal polynomials, and convergence of Wall's continued fractions in Im32 ${L^2{(\#120139 )}}$ , in: J. Approx. Theory, 2001, vol. 108, no 2, p. 161–248.
A. Kuijlaars, K. McLaughlin, W. Van Assche, M. Vanlessen.
The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1, 1] , 2004, vol. 188, no 2, p. 337-398.
J. Leblond, C. Paduret, S. Rigat, M. Zghal.
Sources localisation in ellipsoids by best meromorphic approximation in planar sections, in: Inverse Problems, 2008, vol. 24, no 3, (20p.) p.
V. Lunot, L. Baratchart, S. Kupin, M. Olivi.
Multipoint Schur's algorithm, rational orthogonal functions, asymptotic properties and Schur rational approximation, INRIA, 2008, no RR-6620, Rapport de recherche.
V. Lunot.
Techniques d'approximation rationnelle en synthèse fréquentielle : problème de Zolotarov et algorithme de Schur, Univ. Provence, 2008, PhD Thesis.
V. Lunot, F. Seyfert, S. Bila, A. Nasser.
Certified Computation of Optimal Multiband Filtering Functions, in: IEEE Transactions on Microwave Theory and Techniques, 2008, vol. 56, no 1, p. 105-112
V. Lunot, F. Seyfert, P. Lenoir, A. Nasser, S. Bila, S. Verdeyme.
Synthesis and design of multi-band bandpass filters for space applications, in: CNES-ESA International Workshop on Microwave Filters, 2006.
R. J. McCann.
Polar factorization of maps on Riemannian manifolds, in: Geom. Funct. Anal., 2001, vol. 11, no 3, p. 589–608
G. Monge.
Mémoire sur la théorie des déblais et des ramblais, in: Histoire de l'Académie Royale des Sciences, 1781, p. 666-704
V. V. Peller.
Hankel Operators and their Applications, Springer, 2003.
E. B. Saff, V. Totik.
Logarithmic potentials with external fields, Grundlehren der mathematischen Wissenshaften, Springer, 1997, vol. 316.
F. Seyfert.
Problèmes extrémaux dans les espaces de Hardy, Application à l'identification de filtres hyperfréquences à cavités couplées, Ecole de Mines de Paris, 1998, Ph. D. Thesis.
E. M. Stein.
Harmonic Analysis, Princeton University Press, 1993.
G. Strang, T. Nguyen.
Wavelets and Filter Banks, Wellesley-Cambridge Press, 1997.