V. M. Adamjan, D. Z. Arov, and M. G. Krein, ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM, Mathematics of the USSR-Sbornik, vol.15, issue.1, pp.31-73, 1971.
DOI : 10.1070/SM1971v015n01ABEH001531

L. Baratchart, Approximants for Linear Systems, IMA Journal of Mathematical Control and Information, vol.3, issue.2-3, pp.89-101, 1986.
DOI : 10.1093/imamci/3.2-3.89

L. Baratchart, On the topological structure of inner functions and its use in identification of linear systems, Analysis of Controlled Dynamical Systems of Progress in Systems and Control Theory, pp.51-59, 1991.
DOI : 10.1007/978-1-4612-3214-8_5

L. Baratchart, Rational and meromorphic approximation in L p of the circle: system-theoretic motivations , critical points and error rates, Proceedings of the Third CMFT Conference ? Computational Methods and Function Theory of Series in Approximations and Decompositions, pp.45-78, 1997.

L. Baratchart, F. Mandrèa, E. B. Saff, and F. Wielonsky, 2-D inverse problems for the Laplacian: A meromorphic approximation approach, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.1, pp.1-41, 2006.
DOI : 10.1016/j.matpur.2005.12.001

L. Baratchart and F. Seyfert, An Lp Analog to AAK Theory for p???2, Journal of Functional Analysis, vol.191, issue.1, pp.52-122, 2002.
DOI : 10.1006/jfan.2001.3860

L. Baratchart, H. Stahl, and F. Wielonsky, Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in L 2 of the Circle, Constructive Approximation, vol.17, issue.1, pp.103-138, 2001.
DOI : 10.1007/s003650010017

L. Baratchart, M. Yattselev, and H. Stahl, Weighted extremal domains and best rational approximation, Advances in Mathematics, vol.229, issue.1, pp.357-407, 2012.
DOI : 10.1016/j.aim.2011.09.005

URL : https://hal.archives-ouvertes.fr/hal-00665834

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2011.
DOI : 10.1007/978-0-387-70914-7

F. Demengel and G. Demengel, Espaces fonctionnels, Utilisation dans la résolution des équations aux dérivées partielles, 2007.

D. Deschrijver, B. Haegeman, and T. Dhaene, Orthonormal Vector Fitting: A Robust Macromodeling Tool for Rational Approximation of Frequency Domain Responses, IEEE Transactions on Advanced Packaging, vol.30, issue.2, pp.216-225, 2007.
DOI : 10.1109/TADVP.2006.879429

V. D. Erohin, On the best approximation of analytic functions by rational functions with free poles, Doklady Akademii Nauk SSSR, vol.128, pp.29-32, 1959.

P. Fulcheri and M. Olivi, Approximation: A Gradient Algorithm Based on Schur Analysis, SIAM Journal on Control and Optimization, vol.36, issue.6, pp.2103-2127, 1998.
DOI : 10.1137/S0363012995284230

URL : https://hal.archives-ouvertes.fr/inria-00074158

J. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol.96, 1981.

K. Glover, -error bounds???, International Journal of Control, vol.127, issue.6, pp.1115-1193, 1984.
DOI : 10.1109/TIT.1961.1057636

URL : https://hal.archives-ouvertes.fr/in2p3-00956389

I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, volume 18 of Translations of Mathematical Monographs, 1969.

A. A. Gonchar and E. A. Rakhmanov, EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS, English translation in Mathematics of the USSR-Sbornik, pp.306-352, 1987.
DOI : 10.1070/SM1989v062n02ABEH003242

M. Grant and S. Boyd, Graph Implementations for Nonsmooth Convex Programs, Recent Advances in Learning and Control, pp.95-110, 2008.
DOI : 10.1007/978-1-84800-155-8_7

M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.0 beta, 2013.

V. Guillemin and A. Pollack, Differential Topology, 1974.
DOI : 10.1090/chel/370

B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting, IEEE Transactions on Power Delivery, vol.14, issue.3, pp.1052-1061, 1999.
DOI : 10.1109/61.772353

E. J. Hannan and M. Deistler, The statistical theory of linear systems, 1988.

B. Hanzon and R. Peeters, Balanced Parametrizations of Stable SISO All-Pass Systems in Discrete Time, Mathematics of Control, Signals, and Systems, vol.13, issue.3, pp.240-276, 2000.
DOI : 10.1007/PL00009869

L. Hermans and H. Van-der-auweraer, MODAL TESTING AND ANALYSIS OF STRUCTURES UNDER OPERATIONAL CONDITIONS: INDUSTRIAL APPLICATIONS, Mechanical Systems and Signal Processing, vol.13, issue.2, pp.193-216, 1999.
DOI : 10.1006/mssp.1998.1211

S. Lefteriu and A. C. Antoulas, On the Convergence of the Vector-Fitting Algorithm, IEEE Transactions on Microwave Theory and Techniques, vol.61, issue.4, pp.1435-1443, 2013.
DOI : 10.1109/TMTT.2013.2246526

A. L. Levin, THE DISTRIBUTION OF POLES OF RATIONAL FUNCTIONS OF BEST APPROXIMATION AND RELATED QUESTIONS, Mathematics of the USSR-Sbornik, pp.267-274, 1969.
DOI : 10.1070/SM1969v009n02ABEH002051

L. Ljung, System identification: Theory for the user, 1987.

N. K. Nikolskii, Treatise on the shift operator, volume 273 of Grundlehren der mathematischen Wissenschaften, 1986.

N. K. Nikolskii, Operators, Functions, and Systems: An Easy Reading. Volumes I & II, volume 92-93 of Mathematical Surveys and Monographs, 2002.

M. Olivi, F. Seyfert, and J. Marmorat, Identification of microwave filters by analytic and rational approximation, Automatica, vol.49, issue.2, pp.317-325, 2013.
DOI : 10.1016/j.automatica.2012.10.005

URL : https://hal.archives-ouvertes.fr/hal-00753824

O. G. Parfenov, Estimates of the singular numbers of the Carleson imbedding operator Matematicheskii Sbornik, English translation in Mathematics of the USSR-Sbornik, pp.501-518, 1986.

J. R. Partington, Interpolation, identification, and sampling, 1997.

V. V. Peller, Hankel Operators and their Applications, 2003.
DOI : 10.1007/978-0-387-21681-2

V. A. Prokhorov, On Lp-Generalization of a Theorem of Adamyan, Arov, and Kre??n, Journal of Approximation Theory, vol.116, issue.2, pp.380-396, 2002.
DOI : 10.1006/jath.2002.3677

P. A. Regalia, Adaptive IIR Filtering in Signal Processing and Control, 1995.

P. A. Regalia and M. Mboup, Undermodeled adaptive filtering: an a priori error bound for the Steiglitz-McBride method, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, pp.105-116, 1996.
DOI : 10.1109/82.486457

P. A. Regalia, M. Mboup, and M. Ashari, On the existence of stationary points for the Steiglitz-McBride algorithm, IEEE Transactions on Automatic Control, vol.42, issue.11, pp.421592-1596, 1997.
DOI : 10.1109/9.649730

F. Riesz, B. Sz, and . Nagy, Functional analysis, 1990.

W. Rudin, Real and complex analysis, 1982.

H. Stahl, The structure of extremal domains associated with an analytic function. Complex Variables, Theory and Application, An International Journal, vol.4, issue.4, pp.339-356, 1985.

K. Steiglitz and L. E. Mcbride, A technique for the identification of linear systems, IEEE Transactions on Automatic Control, vol.10, issue.4, pp.461-464, 1965.
DOI : 10.1109/TAC.1965.1098181

V. Totik, A note on rational L p approximation on Jordan curves. Computational Methods and Function Theory, pp.425-431, 2013.

M. Yu and Y. Wang, Synthesis and Beyond, IEEE Microwave Magazine, vol.12, issue.6, pp.62-76, 2011.
DOI : 10.1109/MMM.2011.942008

E. Zeidler, Nonlinear Functional Analysis and its Applications III, 1985.

E. Zeidler, Nonlinear Functional Analysis and its Applications II/A, 1990.