L. Baratchart, J. Grimm, J. Leblond, M. Olivi, F. Seyfert et al., Identification d'un filtre hyperfréquences par approximation dans le domaine complexe, INRIA technical report, 1998.

L. Baratchart, J. Grimm, J. Leblond, and J. R. Partington, Asymptotic estimates for interpolation and constrained approximation in H 2 by diagonalization of toeplitz operators. Integral equations and operator theory, vol.45, pp.269-299, 2003.

L. Baratchart and J. Leblond, Hardy approximation to L p functions on subsets of the circle with 1 ? p < ?. Constructive Approximation, vol.14, pp.41-56, 1998.

L. Baratchart, J. Leblond, and J. R. Partington, Hardy approximation to L ? functions on subsets of the circle, Constructive Approximation, vol.12, pp.423-436, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00074299

L. Baratchart, J. Leblond, and J. R. Partington, Problems of Adamjan-Arov-Krein type on subsets of the circle and minimal norm extensions, Constructive Approximation, vol.16, pp.333-357, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00073354

L. Baratchart, S. Chevillard, and F. Seyfert, On transfer functions realizable with active electronic components, INRIA, vol.36, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01098616

J. M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization, CMS Books in Math. Can. Math. Soc, 2006.

E. W. Cheney, Introduction to approximation theory, 1982.

J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback Control Theory, 1992.

P. L. Duren, Theory of H p spaces, 1970.

J. B. Garnett, Bounded analytic functions, 1981.

M. G. Krein and P. Y. , Nudel'man. Approximation of L 2 (? 1 , ? 2 ) functions by minimum-energy transfer functions of linear systems, Problemy Peredachi Informatsii, vol.11, issue.2, pp.37-60, 1975.

J. Leblond and J. R. Partington, Constrained approximation and interpolation in hilbert function spaces, J. Math. Anal. Appl, vol.234, issue.2, pp.500-513, 1999.

M. Olivi, F. Seyfert, and J. Marmorat, Identification of microwave filters by analytic and rational h 2 approximation, Automatica, vol.49, issue.2, pp.317-325, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00753824

J. Partington, Linear operators and linear systems, 2004.

R. Pintelon, Y. Rollain, and J. Schoukens, System Identification: A Frequency Domain Approach, 2012.

W. Rudin, Real and complex analysis, 1987.

A. Schneck, Constrained optimization in hardy spaces, 2009.

F. Seyfert, Problèmes extrémaux dans les espaces de Hardy. These de Doctorat, 1998.

R. S. Adve, T. K. Sarkar, S. M. Rao, E. K. Miller, and R. Pflug, Application of the Cauchy method for extrapoling/interpolating narrow-band system responses, IEEE Transactions on Microwave Theory and Techniques, vol.45, pp.837-845, 1997.

D. Alpay, L. Baratchart, and A. Gombani, On the differential structure of matrix-valued rational inner functions, Operator Theory: Advances and Applications, vol.73, pp.30-66, 1994.

J. D. Aplevich, Gradient methods for optimal linear system reduction, Int. J. Control, vol.18, 1973.

J. A. Ball, I. Gohberg, and L. Rodman, Interpolation of rational matrix functions, of Operator Theory: Advances and Applications, vol.45, 1990.

L. Baratchart, Existence and generic properties for L 2 approximants of linear systems, I.M.A. Journal of Math. Control and Identification, vol.3, pp.89-101, 1986.

L. Baratchart, M. Cardelli, and M. Olivi, Identification and rational L 2 approximation: a gradient algorithm, Automatica, vol.27, issue.2, pp.413-418, 1991.

L. Baratchart and J. Leblond, Hardy approximation to L p functions on subsets of the circle with 1 ? p < ?. Constructive Approximation, vol.14, pp.41-56, 1998.

L. Baratchart, J. Leblond, J. R. Partington, and N. Torkhani, Robust identification from band-limited data, IEEE Trans. on Atom. Control, vol.42, issue.9, pp.1318-1325, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00074187

L. Baratchart, J. Leblond, and F. Seyfert, Extremal problems of mixed type in H 2 of the circle, 2009.

L. Baratchart and M. Olivi, Critical points and error rank in best H 2 matrix rational approximation, Constructive Approximation, vol.14, pp.273-300, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00073728

P. Van-dooren, K. A. Gallivan, and P. , H 2 -optimal model reduction of MIMO systems, Applied Mathematics Letters, vol.21, 2008.

H. Dym, J-contractive matrix functions, reproducing kernel spaces and interpolation, CBMS lecture notes, vol.71, 1989.

P. Fuhrmann and U. Helmke, Homeomorphism between observable pairs and conditioned invariant subspaces. Systems and Control Letters, vol.30, pp.217-223, 1997.

P. Fulcheri and M. Olivi, Matrix rational H 2 -approximation: a gradient algorithm based on Schur analysis, SIAM Journal on Control and Optimization, vol.36, issue.6, pp.2103-2127, 1998.
URL : https://hal.archives-ouvertes.fr/inria-00074158

K. Glover, All optimal Hankel norm approximations of linear multivariable systems and their L ? -error bounds, Int. J. Contr, vol.39, pp.1115-1193, 1984.

S. Gugercin, A. C. Antoulas, and C. Beattie, H 2 model reduction for large-scale linear dynamical systems, SIAM J. Matrix Anal. Appli, vol.30, 2008.

B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting, IEEE Trans. Power Delivery, vol.14, issue.3, pp.1052-1061, 1999.

B. Gustavsen and A. Semlyen, A robust approach for system identification in the frequency domain, IEEE Trans. Power Delivery, vol.19, issue.3, pp.1167-1173, 2004.

B. Hanzon and J. M. Maciejowski, Constructive algebra methods for the L 2 -problem for stable linear systems, Automatica, vol.32, issue.12, 1996.

B. Hanzon, M. Olivi, and R. L. Peeters,

A. Suarez, Check the stability: Stability analysis methods for microwave circuits, Microwave Magazine, IEEE, vol.16, pp.69-90, 2015.

A. Suarez and R. Quere, Stability analysis of nonlinear microwave circuits, 2002.

J. Jugo, J. Portilla, A. Anakabe, A. Suarez, and J. Collantes, Closedloop stability analysis of microwave amplifiers, Electronics Letters, vol.37, issue.4, pp.226-228, 2001.

J. Collantes, I. Lizarraga, A. Anakabe, and J. Jugo, Stability verification of microwave circuits through floquet multiplier analysis, Circuits and Systems, vol.2, pp.997-1000, 2004.

J. Partington, Linear operators and linear systems, ser. Student texts, London Math. Soc, issue.60, 2004.

L. Baratchart, S. Chevillard, and F. Seyfert, On transfer functions realizable with active electronic components. hal-01098616. Inria Sophia Antipolis, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01098616

W. Rudin, Real and Complex analysis, 1982.

G. A. Baker and P. Graves-morris, Padé Approximants, ser. Encyclopedia of Mathematics and its Applications, vol.59, 1996.

, Spurious Poles in Diagonal Rational Approximation, ser. Series in Computational Mathematics, vol.19, 1992.

H. Stahl, Spurious poles in padé approximation, Journal of Computational and Applied Mathematics, issue.99, 1998.

S. G. Gonnet and L. N. Trefethen, Robust padé approximation via svd, SIAM Rev, vol.55, pp.101-117, 2013.

B. Beckermann and A. Matos, Algebraic properties of robust padé approximants, Jour. Approx. Theory, vol.190, pp.91-115, 2015.

A. Lefteriu and A. C. Antoulas, On the convergence of the vector fitting algorithm, IEEE Transactions on Microwave Theory and Techniques, vol.61, issue.4, 2013.

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

A. Anakabe, N. Aylloon, J. Collantes, A. Mallet, G. Soubercaze-pun et al., Automatic pole-zero identification for multivariable largesignal stability analysis of rf and microwave circuits, Microwave Conference (EuMC), pp.477-480, 2010.

. Amcad and . Engineering, STAN tool -Stability Analysis

I. Mallet, A. Ankabe, G. Soubercaze-pun, and J. Collantes, Automation of the zero-pole identification methods for the stab analysis of microwave active circuits, U.S. Patent, vol.8, pp.637-639, 2013.

M. Van-heijningen, A. P. De-hek, F. E. Van-vliet, and S. Dellier, Stability analysis and demonstration of an x-band gan power amplifier mmic, 2016 11th European Microwave Integrated Circuits Conference (EuMIC), pp.221-224, 2016.

N. Otegi, A. Anakabe, J. Pelaz, J. Collantes, and G. Soubercaze-pun, Experimental characterization of stability margins in microwave amplifiers, IEEE Transactions on, vol.60, issue.12, pp.4145-4156, 2012.

J. Collantes, N. Otegi, A. Anakabe, N. Ayllon, A. Mallet et al., Monte-carlo stability analysis of microwave amplifiers, Wireless and Microwave Technology Conference (WAMICON), pp.1-6, 2011.

N. Ayllon, J. M. Collantes, A. Anakabe, I. Lizarraga, G. Soubercaze-pun et al., Systematic approach to the stabilization of multitransistor circuits, IEEE Tran. on Microwave Theory and Techniques, vol.59, issue.8, pp.2073-2082, 2011.

R. J. Cameron, M. Yu, and Y. Wang, Direct-coupled microwave filters with single and dual stopbands, IEEE Trans. Microw. Theory Tech, vol.53, issue.11, pp.3288-3297, 2005.

G. Macchiarella and S. Tamiazzo, Design techniques for dual-passband filters, IEEE Trans. Microw. Theory Tech, vol.53, issue.11, pp.3265-3271, 2005.

S. Amari, Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique, IEEE Trans. Microw. Theory Tech, vol.48, issue.9, pp.1559-1563, 2000.

M. Mokhtaari, J. Bornemann, K. Rambabu, and S. Amari, Couplingmatrix design of dual and triple passband filters, IEEE Trans. Microw. Theory Tech, vol.54, issue.11, pp.3940-3946, 2006.

V. Lunot, S. Bila, and F. Seyfert, Optimal synthesis for multi-band microwave filters, IEEE MTT-S Int. Microw. Symp. Dig, pp.115-118, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00198990

R. J. Cameron, General coupling matrix synthesis methods for Chebyshev filtering functions, IEEE Trans. Microw. Theory Tech, vol.47, issue.4, pp.433-442, 1999.

E. W. Cheney, Approximation Theory, 1982.

D. Braess, Nonlinear Approximation Theory, 1986.

S. Bila, R. J. Cameron, P. Lenoir, V. Lunot, and F. Seyfert, Chebyshev synthesis for multi-band microwave filters, IEEE MTT-S Int. Microw. Symp. Dig, pp.1221-1224, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00154049

S. Bila, D. Baillargeat, S. Verdeyme, M. Aubourg, P. Guillon et al., Direct electromagnetic optimization of microwave filters, IEEE Micro, vol.2, issue.1, pp.46-51, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00663499

R. J. Cameron, J. C. Faugère, and F. Seyfert, Coupling matrix synthesis for a new class of microwave filter configuration, IEEE MTT-S Int. Microw. Symp. Dig, pp.119-122, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00663550

R. J. Cameron, A. R. Harish, and C. J. Radcliffe, Synthesis of advanced microwave filters without diagonal cross-couplings, IEEE Trans Microwave Theory Tech MTT, vol.50, pp.2862-2872, 2002.

G. Macchiarella, A powerful tool for the synthesis of prototype filters with arbitrary topology, 2003.

, IEEE MTT-S Int Microwave Symp Dig, vol.3, pp.1721-1724, 2003.

S. Amari, Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique, IEEE Trans Microwave Theory Tech MTT, vol.48, pp.1559-1564, 2000.

, International Journal of RF and Microwave Computer-Aided Engineering

R. J. Cameron, J. C. Faugere, and F. Seyfert, Coupling matrix synthesis for a new class of microwave filter configuration, IEEE MTT-S Int Microwave Symp Dig, pp.119-122, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00663550

T. Kailath, Upper Saddle River, NJ, 1980.

D. Cox, J. Little, and D. O'shea, Ideals, varieties, and algorithms, 1997.

L. Gonzalez-vega, F. Rouillier, and M. F. Roy, Some tapas of computer algebra, Algorithms and computation in mathematics, vol.4, pp.34-65, 1999.

J. C. Faugere, A new efficient algorithm for computing Groebner bases without reduction to zero (F5), Proc Int Symp on Symbolic and Algebraic Comp, pp.75-83, 2002.

R. J. Cameron, General coupling matrix synthesis method for Chebyshev filtering functions, IEEE Trans Microwave Theory Tech MTT, vol.47, pp.433-442, 1999.

F. Seyfert, L. Baratchart, J. P. Marmorat, S. Bila, and J. Sombrin, Extraction of coupling parameters for microwave filters: Determination of a stable rational model from scattering data, IEEE MTT-S Int Microwave Symp Dig, vol.1, pp.25-28, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00504779

R. V. Snyder, Practical aspects of microwave filter development, IEEE Microwave Mag, vol.8, issue.2, pp.42-54, 2007.

C. Kudsia, R. Cameron, and W. C. Tang, Innovation in microwave filters and multiplexing networks for communications satellite systems, IEEE Trans. Microwave Theory Tech, vol.40, issue.6, pp.1133-1149, 1992.

R. Levy, R. V. Snyder, and G. L. Matthaei, Design of microwave filters, IEEE Trans. Microwave Theory Tech, vol.50, issue.3, pp.783-793, 2002.

G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks and Coupling Structures, 1964.

D. Swanson and G. Macchiarella, Microwave filter design by synthesis and optimization, IEEE Microwave Mag, vol.8, issue.2, pp.55-69, 2007.

H. C. Bell, The coupling matrix in low-pass prototype filters, IEEE Microwave Mag, vol.8, issue.2, pp.70-76, 2007.

A. E. Atia and A. E. Williams, Narrow-bandpass waveguide filters, IEEE Trans. Microwave Theory Tech, vol.20, issue.4, pp.258-265, 1972.

R. Cameron, Synthesis of advanced microwave filters without diagonal cross-couplings, IEEE Trans. Microwave Theory Tech, vol.50, issue.12, pp.2862-2871, 2002.

R. Cameron, General coupling matrix synthesis methods for Chebyshev filtering functions, IEEE Trans. Microwave Theory Tech, vol.47, issue.4, pp.433-442, 1999.

S. Amari, Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique, IEEE Trans. Microwave Theory Tech, vol.48, issue.9, pp.1559-1564, 2000.

M. Yu, W. Tang, A. Malarky, V. Dokas, R. Cameron et al., Predistortion technique for cross-coupled filters and its application to satellite communication systems, IEEE Trans. Microwave Theory Tech, vol.51, issue.12, pp.2505-2515, 2003.

V. Lunot, S. Bila, and F. Seyfert, Optimal synthesis for multiband microwave filters, 2007 IEEE MTT-S Int. Microwave Symp. Dig, pp.115-118, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00198990

F. Seyfert, From S to M" tutorial

H. C. Bell, Canonical asymmetric coupled-resonator filters, IEEE Trans. Microwave Theory Tech, vol.30, pp.1335-1340, 1982.

S. Amari, On the maximum number of finite transmission zeros of coupled resonator filters with a given topology, IEEE Microwave Guided Wave Lett, vol.9, issue.9, pp.354-356, 1999.

R. Cameron, J. C. Faug`ere, F. Roullier, and F. Seyfert, Exhaustive approach to the coupling matrix synthesis problem and application to the design of high degree asymmetric filters, Int. J. RF Microwave Computer Aided Eng, vol.17, issue.1, pp.4-12, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00663777

W. A. Atia, K. Zaki, and A. E. Atia, Synthesis of general topology multiple coupled resonators filters by optimization, IEEE MTT-S Int. Symp. Dig, vol.2, pp.1693-1698, 1998.

S. Tamiazzo and G. Macchiarella, An analytical technique for the synthesis of cascaded N-tuplets cross-coupled resonators microwave filters using matrix rotations, IEEE Trans. Microwave Theory Tech, vol.53, issue.5, pp.1693-1698, 2005.

-. Dedale and . Page,

P. Lenoir, S. Bila, F. Seyfert, D. Baillargeat, and S. Verdeyme, Synthesis of assymetrical dual-band bandpass filter based on equivalent network simplification, IEEE Trans. Microwave Theory Tech, vol.54, issue.7, pp.3090-3097, 2006.

H. L. , Computer-aided filter alignment and diagnosis, IEEE Trans. Microwave Theory Tech, vol.26, issue.12, pp.958-963, 1978.

A. Garcia-lamperez, S. Llorente-romano, M. Salazar-palma, and T. K. Sarkar, Efficient electromagnetic optimization of microwave filters and multiplexers using rational models, IEEE Trans. Microwave Theory Tech, vol.52, issue.2, pp.508-521, 2004.

P. Kozakowski and M. Mrozowski, Quadratic programming approach to coupled resonator filter CAD, IEEE Trans. Microwave Theory Tech, vol.54, issue.11, pp.3906-3913, 2006.

S. Bila, D. Baillargeat, M. Aubourg, S. Verdeyme, P. Guillon et al., Direct electromagnetic optimization of microwave filters, IEEE Microwave Mag, vol.2, issue.1, pp.46-51, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00663499

P. Harscher, R. Vahldieck, and S. Amari, Automated filter tuning using generalized low-pass prototype networks and gradientbased parameter extraction, IEEE Trans. Microwave Theory Tech, vol.49, issue.12, pp.2532-2538, 2001.

F. Seyfert, L. Baratchart, J. P. Marmorat, S. Bila, and J. Sombrin, Extraction of coupling parameters for microwave filters: Determination of a stable rational model from scattering data, IEEE MTT-S Int. Microwave Symp. Dig, pp.25-28, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00504779

F. T. Hsu, Z. Zhang, K. A. Zaki, and A. E. Atia, Parameter extraction for symmetric coupled-resonator filters, IEEE Trans. Microwave Theory Tech, vol.50, issue.12, pp.2971-2978, 2002.

R. J. Cameron, Dual-mode realisation for asymmetric filter characteristics, ESA J, vol.6, issue.3, pp.339-356, 1982.

S. Holme, Multiple passband filters for satellite applications, Proc. 20th AIAA Int, pp.1993-1996, 2002.

R. J. Cameron, General coupling matrix synthesis methods for Chebyshev filtering functions, IEEE Trans. Microw. Theory Tech, vol.47, issue.4, pp.433-442, 1999.

G. Macchiarella and S. Tamiazzo, A design technique for symmetric dualband filters, IEEE MTT-S Int. Microw. Symp. Dig, vol.4, p.pp, 2005.

J. Lee, M. S. Uhm, and I. B. Yom, A dual-passband filter of canonical structure for satellite applications, IEEE Microw. Wireless Compon. Lett, vol.14, issue.6, pp.271-273, 2004.

J. Lee, M. S. Uhm, and J. S. Park, Synthesis of self-equalized dualpassband filter, IEEE Microw. Wireless Compon. Lett, vol.15, issue.4, pp.256-258, 2005.

P. Lenoir, S. Bila, D. Baillargeat, and S. Verdeyme, Design of dualband bandpass filters for space applications, Eur. Microw. Assoc, 2005.

R. J. Cameron, A. R. Harish, and C. J. Radcliffe, Synthesis of advanced microwave filters without diagonal cross-couplings, IEEE Trans. Microw. Theory Tech, vol.50, issue.12, pp.2862-2872, 2002.

F. Seyfert, R. Cameron, and J. C. Faugère, Coupling matrix synthesis for a new class of microwave filter configuration, IEEE MTT-S Int
URL : https://hal.archives-ouvertes.fr/hal-00663550

. Microw, . Symp, and . Dig, , vol.4, 2005.

S. Bila, D. Baillargeat, S. Verdeyme, F. Seyfert, L. Baratchart et al., Simplified design of microwave filters with asymmetric transfer functions, Eur. Microw. Conf, pp.1357-1360, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00663524

P. Harsher, R. Vahldieck, and S. Amari, Automated filter tuning using generalized low-pass prototype networks and gradient-based parameter extraction, IEEE Trans. Microw. Theory Tech, vol.49, issue.12, pp.2532-2538, 2001.

M. Kahrizi, S. Safavi-naeini, S. K. Chaudhuri, and R. Sabry, Computer diagnosis and tuning of RF and microwave filters using modelbased parameter estimation, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl, vol.49, issue.9, pp.1263-1270, 2002.

S. Bila, D. Baillargeat, M. Aubourg, S. Verdeyme, F. Seyfert et al., Finite element modelling for the design optimization of microwave filters, IEEE Trans. Magn, vol.40, issue.2, pp.472-475, 2004.

, Recall that a map is called proper if the preimage of a compact set is compact. PROPOSITION 6, The map ? : PM N ? D m × P + Z

, By the continuity of ?, W is closed. Thus, it remains to prove that W is bounded in PM N . Assume for a contradiction that there is an unbounded sequence p n in ? ?1 (K), and let us write ?(p n ) = Proof. (of Theorem 10) If m > 0, then pp * + rr * cannot vanish at x 1 since r, Proof. Let K ? D m × P + be compact and put W = ? ?1 (K)

, To secure the choice of ? , as p j , q j are no longer monic, we trade the requirement made in Proposition 5 construction. Then, reasoning as in Proposition 7 shows that? is a homeomorphism. Finally, let PN(r) ? PN be the subset of polynomials having no common real root with r including at infinity, which is easily seen to be open

M. Abrahamse, The Pick interpolation theorem for finitely connected domains, Michigan Math. J, vol.26, pp.195-203, 1979.

J. and J. E. Mccarthy, Journal für die reine und angewandte Mathematik, vol.506, pp.191-124, 1999.

J. J. Agler-and-n and . Young, Boundary Nevanlinna-Pick interpolation via reduction and augmentation, Mathematische Zeitschrift, vol.268, pp.791-817, 2011.

A. Arias-and-g and . Popescu, Noncommutative interpolation and poisson transforms, Israel J. Math, vol.115, pp.205-234, 2000.

J. Ball, I. Gohberg, and A. L. Rodman, Interpolation of Rational Matrix Functions, vol.45, 1990.

J. A. Ball-and-v and . Bolotnikov, Nevanlinna-Pick interpolation for Schur-Agler class functions on domains with matrix polynomial defining function, New York J. Math, p.11, 2005.

J. A. Ball-and-v and . Bolotnikov, Interpolation in the noncommutative Schur-Agler class, J. Operator Theory, vol.58, pp.83-126, 2007.

J. A. Ball-and-s.-ter and . Horst, Robust Control, Multidimensional Systems and Multivariable Nevanlinna-Pick Interpolation, vol.203, pp.13-88, 2010.

L. Baratchart, S. Chevillard, and A. T. Qian, Minimax principle and lower bounds in H 2 -rational approximation, Journal of Approximation Theory, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00922815

L. Baratchart-and-m and . Olivi, Critical points and error rank in best H 2 matrix rational approximation, Constructive Approximation, vol.14, pp.273-300, 1998.

L. Baratchart, M. Olivi, and A. F. Seyfert, Generalized Nevanlinna-Pick interpolation on the boundary. Application to impedance matching, Proceedings of the MTNS, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00920564

V. Belevitch, Elementary applications of scattering formalism to network design, IRE Transactions on Circuit Theory, vol.3, pp.97-104, 1956.

V. Belevitch, Classical Network Theory, 1968.

C. Byrnes, T. Georgiou, and A. A. Lindquist, A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint, IEEE Transactions on Automatic Control, vol.46, pp.822-839, 2001.

C. Byrnes, T. T. Georgiou, A. Lindquist, and A. A. Megretski, Generalized interpolation in H ? with a complexity constraint, Trans. Amer. Math. Soc, vol.358, pp.965-988, 2006.

H. Carlin-and-p, W. Civalleri, and . Circuit-design, , 1997.

K. R. Davidson-and-d and . Pitts, Nevanlinna-Pick interpolation for noncommutative analytic Toeplitz algebras, Integral Equations and Operator Theory, vol.31, pp.321-337, 1998.

, Antenna reflexion L 1,1 and global reflexion G, vol.1, p.1

H. Dym, J-contractive matrix functions, reproducing kernel spaces and interpolation, vol.71, 1989.

B. A. Francis, J. Helton, and A. G. Zames, H ? -optimal feedback controllers for linear multivariable systems, IEEE Transactions on Automatic Control, vol.29, pp.888-900, 1984.

P. Fuhrmann, Linear Systems and Operators in Hilbert Spaces, 1981.

J. Garnett, Bounded Analytic Functions, 1981.

T. Georgiou, A topological approach to Nevanlinna-Pick interpolation, SIAM J. Math. Anal, vol.18, issue.5, pp.1248-1260, 1987.

T. Georgiou, The interpolation problem with a degree constraint, IEEE Transactions on Automatic Control, 1999.

V. A. Guillemin, D. Pollack, and . Topology, , 1974.

J. Helton, Broadbanding:gain equalization directly from data, IEEE Transactions on Circuits and Systems, vol.28, pp.1125-1137, 1981.

T. T. Karlsson-and-a and . Lindquist, The inverse problem of analytic interpolation with degree constraint and weight selection for control synthesis, IEEE Transactions on Automatic Control, vol.55, pp.405-418, 2010.

R. Kalman, P. Falb, and A. A. Arbib, Topics in Mathematical System Theory, 1969.

P. Khargonekar-and-a and . Tannenbaum, Noneuclidean metrics and the robust stabilization of systems with parameter uncertainty, IEEE Transactions on Automatic Control, vol.30, pp.1005-1013, 1985.

H. Kimura, Directional interpolation approach to H ? -optimization and robust stabilization, IEEE Transactions on Automatic Control, vol.32, pp.1095-1093, 1987.

H. Kimura, Conjugation, interpolation and model-matching in H ?, Int. J. Control, vol.49, pp.269-307, 1989.

D. J. Limebeer-and-b and . Anderson, An interpolation theory approach to H ? controller degree bounds, Linear Algebra and its Applications, vol.98, pp.347-386, 1988.

J. Munkres, Elements of algebraic topology, 1984.

Y. G. Delsarte-and-y and . Kamp, On the role of the Nevanlinna-Pick problem in circuit and system theory, Circuit Theory and Appl, vol.9, pp.177-187, 1981.

F. Riesz-and-b and . Sz?kefalvi-nagy, Functional Analysis, 1990.

D. Sarason, Nevanlinna-Pick interpolation with boundary data, Integral Equations Operator Theory, vol.30, pp.231-250, 1998.

M. S. Takyar-and-t and . Georgiou, Analytic interpolation with a degree constraint for matrix-valued functions, IEEE Transactions on Automatic Control, vol.55, pp.1075-1088, 2010.

A. Tannenbaum, Feedback stabilization of linear dynamical plants with uncertainty in the gain factor, Int. Journal Control, vol.32, pp.1-16, 1980.

F. W. Warner, Foundations of Differential Manifolds and Lie Groups, vol.94, 1983.

H. Yong-jian, K. D. Boubakar, and A. C. Gong-ning, On boundary Nevanlinna-Pick interpolation for Carathéodory matrix functions, Linear Algebra and its Applications, vol.423, pp.209-229, 2007.

D. C. Youla-and-m and . Saito, Interpolation with positive real functions, J. Franklin Institute, 1967.

O. A. Zames-and-b and . Francis, Feedback, minimax sensitivity, and optimal robustness, IEEE Transactions on Automatic Control, vol.28, pp.585-600, 1983.

W. Rudin, Real and complex analysis, 1987.

J. Garnett, Bounded Analytic Functions, 1981.

K. Hoffman, Banach spaces of analytic functions, 1962.

P. L. Duren, Theory of H p spaces, 1970.

L. Baratchart, J. Leblond, and J. R. Partington, Hardy approximation to L p functions on subsets of the circle, 1994.
URL : https://hal.archives-ouvertes.fr/inria-00074299

M. G. Krein and P. Y. , Approximation of L 2 (? 1 , ? 2 ) functions by minimum-energy transfer functions of linear systems, Problemy Peredachi Informatsii, vol.11, pp.37-60, 1975.

D. Alpay, L. Baratchart, and J. Leblond, Some extremal problems linked with identification from partial frequency data". In: 10th conference on analysis and optimization of systems, Lect. Notes in Control and Information Sc, vol.185, pp.563-573, 1992.

L. Baratchart and J. Leblond, Hardy approximation to L p functions on subsets of the circle with 1 ? p < ?, Constructive Approximation, vol.14, pp.41-56, 1998.

L. Baratchart, J. Grimm, J. Leblond, M. Olivi, F. Seyfert et al., Identification d'un filtre hyperfréquences par approximation dans le domaine complexe, INRIA technical report, 1998.

F. Seyfert, Problèmes extrémaux dans les espaces de Hardy. Application à l'identification de filtres hyperfréquences à cavités couplées, 1998.

A. Schneck, Constrained Hardy space approximation, Journal of Approximation Theory, vol.162, pp.1466-1483, 2010.

L. Baratchart, J. Leblond, and F. Seyfert, Constrained L 2 -approximation by polynomials on subsets of the circle, New Trends in Approximation Theory. In Memory of André Boivin, vol.81, pp.1-14, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01671183

L. Baratchart, J. Leblond, and F. Seyfert, Constrained extremal problems in H 2 and Carleman's formulae, In: Mat. Sbornik, vol.209, pp.922-957, 2018.

F. Seyfert, M. Olivi, and J. Marmorat,

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, In: Math. USSR Sbornik, vol.15, pp.31-73, 1971.

N. J. Young, An introduction to Hilbert space, 1988.

J. Partington, Linear operators and linear systems. Student texts 60, 2004.

K. Glover, All optimal Hankel norm approximations of linear multivariable systems and their L ? -error bounds, Int. J. Contr, vol.39, pp.1115-1193, 1984.

J. P. Marmorat and M. Olivi, RARL2: a Matlab based software for H 2 rational approximation, 2004.

P. Fulcheri and M. Olivi, Identification and matrix rational H 2 -approximation: a gradient algorithm based on Schur analysis, p.2520, 1995.
URL : https://hal.archives-ouvertes.fr/inria-00074158

M. Olivi, F. Seyfert, and J. Marmorat, Identification of microwave filters by analytic and rational H 2 approximation, Automatica, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00753824

M. Seyfert, G. Oldoni, D. Macchiarella, and . Pacaud, De-embedding response of filters from diplexer measurements, International Journal of RF and Microwave Computer-Aided Engineering, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00763665

F. Seyfert, M. Oldoni, G. Macchiarella, and D. Pacaud, De-embedding response of filters from diplexer measurements, International Journal of RF and Microwave Computer-Aided Engineering
URL : https://hal.archives-ouvertes.fr/hal-00763665

D. , , 2012.

S. Lefteriu, M. Olivi, F. Seyfert, and M. Oldoni, System identification of microwave filters from multiplexers by rational interpolation, Automatica, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01357934

M. Oldoni, G. Macchiarella, and F. Seyfert, Synthesis and Modelling Techniques for Microwave Filters and Diplexers: Advances in Analytical Methods with Applications to Design and Tuning, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01096252

A. Cooman, F. Seyfert, M. Olivi, S. Chevillard, and L. Baratchart, Model-Free Closed-Loop Stability Analysis: A Linear Functional Approach, IEEE Transactions on Microwave Theory and Techniques, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01381731

V. Belevitch, Classical Network Theory, 1968.

H. J. Carlin and P. P. Civalleri, Wideband Circuit Design, 1997.

J. Grimm, Rational approximation of transfer functions in the Hyperion software, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00072642

T. Kailath, Linear Systems, 1980.

P. Fuhrmann, Linear Systems and Operators in Hilbert Spaces, 1981.

R. J. Cameron, R. Mansour, and C. M. Kudsia, Microwave Filters for Communication Systems: Fundamentals, Design and Applications, 2007.

V. Lunot, F. Seyfert, S. Bila, and A. Nasser, Certified computation of optimal multiband filtering functions, IEEE Transactions on Microwave Theory and Techniques, vol.56, pp.105-112, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00663542

V. Lunot, Techniques d'approximation rationnelle en synthèse fréquentielle : problème de Zolotarov et algorithme de Schur, 2008.

A. N. Kolmogorov and A. P. Yushkevich, Mathematics of the 19th Century: Function Theory According to Chebyshev Ordinary Differential Equations Calculus of Variations Theory of Finite Differences. Mathematics of the 19th Century. Birkhäuser Basel, p.9783764358457, 1998.

K. L. Su, Handbook of Tables for Elliptic-Function Filters, p.9780792391098, 1990.

D. Braess, Series in computational mathematics, vol.7, 1986.

M. J. Powell, Approximation Theory and Methods, 1981.

V. Lunot, S. Bila, and F. Seyfert, Optimal synthesis for multi-band microwave filters, IEEE MTT-S International Microwave Symposium Digest, pp.115-118, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00198990

S. Bila, R. J. Cameron, P. Lenoir, V. Lunot, and F. Seyfert, Chebyshev synthesis for multi-band microwave filters, IEEE MTT-S International Microwave Symposium Digest, pp.1221-1224, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00154049

A. Nasser, V. Lunot, S. Bila, D. Baillargeat, S. Verdeyme et al., Design of multiband filters in waveguide technology for space applications, Workshop on Design and Implementation Techniques for Multiband Filters IEEE MTT-S International Microwave Symposium Digest, IMS 2008. Atlanta, United States, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00358460

J. C. Slater, Microwave Electronics, Rev. Mod. Phys, vol.18, pp.441-512, 1946.

K. Kurokawa, An introduction to the theory of microwave circuits, 1969.

R. F. Harrington, Time-Harmonic Electromagnetic Fields. IEEE Press Series on Electromagnetic Wave Theory, p.9780471208068, 2001.

G. L. Matthaei, Microwave filters, impedance-matching networks, and coupling structures, vol.1, 1964.

I. , Hunter and Institution of Electrical Engineers. Theory and Design of Microwave Filters, Electromagnetics and Radar Series. Institution of Engineering and Technology, 2001.

P. Faurre, M. Clerget, and F. Germain, Opérateurs Rationnels positifs. Méthodes Mathématiques de l'Informatique, vol.8, 1979.

R. J. Cameron, General coupling matrix synthesis methods for chebyshev filtering functions, IEEE Transaction on Microwave Theory and Techniques, vol.47, pp.433-442, 1999.

R. J. Cameron, Advanced Filter Synthesis, IEEE Microwave Magazine, vol.12, issue.6, pp.1527-3342, 2011.

R. J. Cameron, A. R. Harish, and C. J. Radcliffe, Synthesis of advanced microwave filters without diagonal cross-couplings, IEEE Transactions on Microwave Theory and Techniques, vol.50, pp.2862-2872, 2002.

S. Tamiazzo and G. Macchiarella, An analytical technique for the synthesis of cascaded N-tuplets cross-coupled resonators microwave filters using matrix rotations, IEEE Transactions on Microwave Theory and Techniques, vol.53, issue.5, pp.1693-1698, 2005.

S. Amari, On the maximum number of finite transmission zeros of coupled resonator filters with a given topology, IEEE Microwave and Guided Wave Letters, vol.9, pp.1051-8207, 1999.

S. Amari, Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique, IEEE Transactions on Microwave Theory and Techniques, vol.48, pp.1559-1564, 2000.

G. Macchiarella, A powerful tool for the synthesis of prototype filters with arbitrary topology, IEEE MTT-S International Microwave Symposium Digest, vol.3, pp.1467-1470, 2003.

A. E. Williams and A. Atia, New type of waveguide bandpass filters for satellite transponders, In: COMSAT Tech. Rev, vol.1, 1971.

W. A. Atia, K. A. Zaki, and A. E. Atia, Synthesis of general topology multiple coupled resonator filters by optimization, IEEE MTT-S International Microwave Symposium Digest (Cat. No.98CH36192), vol.2, pp.821-824, 1998.

K. Kendig, Elementary Algebraic Geometry, vol.44, 1977.

A. Pollack, V. Guillemin, and . Topology, , 1974.

D. A. Cox, J. Little, and D. Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics), p.387356509, 2007.

E. Arbarello and D. Mumford, The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians, Lecture Notes in Mathematics, p.9783540632931, 1999.

R. Igor and . Shafarevich, Basic algebraic geometry, 2013.

J. R. Sendra, F. Winkler, and S. Pérez-diaz, Rational Algebraic Curves: A Computer Algebra Approach, Algorithms and Computation in Mathematics

H. Springer-berlin, , p.9783540737254, 2007.

J. Faugère, FGb: A Library for Computing Gröbner Bases, Mathematical Software -ICMS 2010. Ed. by Komei Fukuda, Joris Hoeven, Michael Joswig, and Nobuki Takayama, vol.6327, pp.84-87, 2010.

, Fabien Seyfert. Software Dedale-HF

R. J. Cameron, J. Faugère, and F. Seyfert, Coupling matrix synthesis for a new class of microwave filter configuration, IEEE MTT-S International Microwave Symposium, vol.1, pp.119-124, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00663550

R. J. Cameron, J. Faugère, F. Rouillier, and F. Seyfert, Exhaustive approach to the coupling matrix synthesis problem and application to the design of high degree asymmetric filters, International Journal of RF and Microwave Computer-Aided Engineering, vol.17, issue.1, pp.4-12, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00663777

F. Seyfert and S. Bila, General synthesis techniques for coupled resonator networks, IEEE Microwave Magazine, vol.8, pp.98-104, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00198658

P. Lenoir, S. Bila, F. Seyfert, D. Baillargeat, and S. Verdeyme, Synthesis and design of asymmetrical dual-band bandpass filters based on equivalent network simplification, IEEE Transactions on Microwave Theory and Techniques, vol.54, pp.3090-3097, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00663496

S. Amari, F. Seyfert, and M. Bekheit, Theory of Coupled Resonator Microwave Bandpass Filters of Arbitrary Bandwidth, IEEE Transactions on Microwave Theory and Techniques, vol.58, pp.2188-2203, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00663513

/. Tmtt, , 2010.

L. Baratchart, M. Olivi, and F. Seyfert, Boundary Nevanlinna-Pick interpolation with prescribed peak points. Application to impedance matching, SIAM Journal on Mathematical Analysis, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01377782

D. Youla, A New Theory of Broad-band Matching, IEEE Transactions on Circuit Theory, vol.11, issue.1, pp.30-50, 1964.

R. M. Fano, Theoretical limitations on the broadband matching of arbitrary impedances, Journal of the Franklin Institute, vol.249, pp.57-83, 1950.

J. and W. Helton, Non-Euclidean functional analysis and electronics, Bull. Amer. Math. Soc. (N.S.), vol.7, issue.1, pp.1-64, 1982.

J. W. Helton, Broadbanding:Gain equalization directly from data, IEEE Transactions on Circuits and Systems, vol.28, pp.98-4094, 1981.

L. Baratchart, M. Olivi, and F. Seyfert, Generalized Nevanlinna-Pick interpolation on the boundary. Application to impedance matching, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00920564

L. V. Ahlfors, Conformal invariants, 1973.

J. Partington, Interpolation, Identification and Sampling, 1997.

T. Georgiou, A topological approach to Nevanlinna-Pick interpolation, SIAM J. Math. Anal, vol.18, issue.5, pp.1248-1260, 1987.

T. Georgiou, The interpolation problem with a degree constraint, IEEE Transactions on Automatic Control, 1999.

A. Linquist, C. Byrnes, and T. Georgiou, A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint, IEEE Transactions on Automatic Control AC, vol.46, pp.822-839, 2001.