]. S. Bibliographie and . Agmon, On the eigenfunctions and the eigenvalues of general elliptic boundary value problem, Comm. Pure Appl. Math, vol.15, issue.1, pp.119-147, 1962.

C. Alves, A. L. Silvestre, T. Takahashi, and M. Tucsnak, Solving inverse source problems using observability, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00283402

D. Auroux, Algorithmes rapides pour le traitement d'images et l'assimilation de données . Mémoire de l'Habilitation à Diriger la Recherche, 2008.

S. A. Avdonin and W. Moran, Simultaneous control problems for systems of elastic strings and beams, Systems & Control Letters, vol.44, issue.2, pp.147-155, 2001.
DOI : 10.1016/S0167-6911(01)00137-2

J. Baillieul and M. Levi, Rotational elastic dynamics, Physica D: Nonlinear Phenomena, vol.27, issue.1-2, pp.43-62, 1987.
DOI : 10.1016/0167-2789(87)90004-2

A. V. Balakrishnan, Compensator design for stability enhancement with collocated controllers, IEEE Transactions on Automatic Control, vol.36, issue.9, pp.994-1007, 1991.
DOI : 10.1109/9.83531

C. Bardos, G. Lebeau, and J. Rauch, Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary, SIAM Journal on Control and Optimization, vol.30, issue.5, pp.1024-1065, 1992.
DOI : 10.1137/0330055

P. Bénilan and H. Touré, Sur l?????quation g??n??rale ut = a(., u, ??(., u)x)x + ?? dans L1 : II. Le probl??me d?????volution, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.12, issue.6, pp.727-761, 1995.
DOI : 10.1016/S0294-1449(16)30149-4

S. K. Biswas and N. U. Ahmed, Optimal control of large space structures governed by a coupled system of ordinary and partial differential equations, Mathematics of Control, Signals, and Systems, vol.3, issue.1, pp.1-18, 1989.
DOI : 10.1007/BF02551358

A. M. Bloch and E. S. Titi, On The Dynamics of Rotating Elastic Beams, Proc. Conf. New Trends System Theory, 1990.
DOI : 10.1007/978-1-4612-0439-8_15

G. Bornard, F. Celle, G. Dauphin-tanguy, G. Gilles, J. Lottin et al., Systèmes non linéaires. 1. modélisation -estimation, chapter Observabilté et observateurs, pp.177-221, 1993.

H. Bounit and H. Hammouri, Bounded feedback stabilization and global separation principle of distributed parameter systems, IEEE Transactions on Automatic Control, vol.42, issue.3, pp.42-3414, 1997.
DOI : 10.1109/9.557588

H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, 1973.

H. Brézis, Analyse Fonctionnelle : Théorie et Applications, 1983.

N. Burq and M. Zworski, Geometric control in the presence of a black box, Journal of the American Mathematical Society, vol.17, issue.02, pp.443-471, 2004.
DOI : 10.1090/S0894-0347-04-00452-7

L. A. Corona, Quelques contributions aux observateurs non linéaires à horizon glissant, Thèse de Doctorat, INPG, 2002.

F. Celle, J. P. Gauthier, D. Kazakos, and G. Sallet, Synthesis of nonlinear observers: A harmonic-analysis approach, Mathematical Systems Theory, vol.13, issue.1, pp.291-322, 1989.
DOI : 10.1007/BF02088304

N. Chafee, Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions, Journal of Differential Equations, vol.18, issue.1, pp.111-134, 1975.
DOI : 10.1016/0022-0396(75)90084-4

G. Chen, S. G. Krants, D. W. Ma, C. E. Wayne, and H. H. West, The Euler-Bernoulli beam equation with boundary energy dissipation. Operator Method For Control Problem, Lecture Notes in Pure and Applied Mathematics, pp.67-96, 1987.

B. Chentouf and J. F. Couchouron, Nonlinear feedback stabilization of a rotating body-beam without damping, ESAIM: Control, Optimisation and Calculus of Variations, vol.4, pp.515-535, 1999.
DOI : 10.1051/cocv:1999120

URL : https://hal.archives-ouvertes.fr/inria-00073115

N. Cîndea, S. Micu, and M. Tucsnak, An approximation method for exact controls of vibrating systems

B. F. Conrad and M. Pierre, Stabilization of Euler-Bernoulli beam by nonlinear boundry feedback, 1990.

J. M. Coron, On the Null Asymptotic Stabilization of the Two-Dimensional Incompressible Euler Equations in a Simply Connected Domain, SIAM Journal on Control and Optimization, vol.37, issue.6, pp.1874-1896, 1999.
DOI : 10.1137/S036301299834140X

R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems, 1978.

R. F. Curtain and G. Weiss, Exponential stabilization of well-posed systems by colocated feedback, SIAM Journal on Control and Optimization, vol.45, issue.1, pp.273-297, 2006.
DOI : 10.1137/040610489

R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, 1995.
DOI : 10.1007/978-1-4612-4224-6

A. J. Deguenon, Observateurs des systèmes anti-adjoints de dimension infinie et applications, Thèse de Doctorat, 2005.

A. J. Deguenon, G. Sallet, and C. Z. Xu, A Luenberger observer for infinite dimensional skew-symmetric systems with application to an elastic beam, Proc. 2nd Int. Symp on Comm. Control and Signal, 2006.

M. Demetriou, Natural second-order observers for second-order distributed parameter systems, Systems & Control Letters, vol.51, issue.3-4, pp.225-234, 2004.
DOI : 10.1016/j.sysconle.2003.08.005

M. Demetriou and F. Fahroo, Model reference adaptive control of structurally perturbed second-order distributed parameter systems, International Journal of Robust and Nonlinear Control, vol.3, issue.16, pp.773-799, 2006.
DOI : 10.1002/rnc.1100

S. Dolecki and D. L. Russell, A General Theory of Observation and Control, SIAM Journal on Control and Optimization, vol.15, issue.2, pp.185-220, 1977.
DOI : 10.1137/0315015

V. and D. Santos, Contrôle frontière par modèle interne de systèmes hyperboliques : application à la régulation de canaux d'irrigation, Thèse de Doctorat, 2004.

P. Dufour, Contribution à la commande prédictive des systèmes à paramètres répartis non linéaires, Thèse de Doctorat, 2000.

L. C. Evans, Partial Differential Equations, Amer. Math. Society, 1998.

K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 1999.
DOI : 10.1007/s002330010042

M. Fliess, J. Lévine, P. Martin, and P. Rouchon, Flatness and defect of nonlinear systems : introductory theory and examples, Int. J. Control, pp.61-61327, 1995.

M. Fliess and H. Mounier, Controllability and observability of linear delay systems: an algebraic approach, ESAIM: Control, Optimisation and Calculus of Variations, vol.3, pp.301-314, 1998.
DOI : 10.1051/cocv:1998111

H. Mounier and M. Fliess, An algebraic framework for infinite dimensional linear systems, E-sta, vol.11, 2004.

M. Fliess, Variations sur la notion de contrôlabilité. Constructive Algebra and Systems Theory, Royal Netherlands Academy of Arts and Sciences, pp.267-305, 2006.

M. Fliess and H. Sira-ramínez, Reconstructeurs d'??tat, Comptes Rendus Mathematique, vol.338, issue.1, pp.91-96, 2004.
DOI : 10.1016/j.crma.2003.11.004

M. Fliess and H. Sira-ramínez, Control via state estimations of some nonlinear systems, Proc. Symp. Nonlinear Control Systems (NOLCOS), 2004.
URL : https://hal.archives-ouvertes.fr/inria-00001096

J. C. Friedly, Dynamic Behavior of Processes, Journal of Dynamic Systems, Measurement, and Control, vol.95, issue.3, 1972.
DOI : 10.1115/1.3426731

J. P. Gauthier and I. Kupka, A separation principle for bilinear systems with dissipative drift, IEEE Transactions on Automatic Control, vol.37, issue.12, pp.1970-1974, 1992.
DOI : 10.1109/9.182484

J. P. Gauthier and C. Z. Xu, -control of a distributed parameter system with non-minimum phase, International Journal of Control, vol.21, issue.1, pp.45-79, 1991.
DOI : 10.1109/TAC.1983.1103275

URL : https://hal.archives-ouvertes.fr/hal-00908679

J. P. Gauthier, C. Z. Xu, and A. Bounabat, An observer for infinite-dimensional skewadjoint bilinear systems, J. Math. Sys., Estimation and Control, vol.8, pp.31-50, 1998.

B. Gebauer and O. Scherzer, Impedance-Acoustic Tomography, SIAM Journal on Applied Mathematics, vol.69, issue.2, pp.565-576, 2008.
DOI : 10.1137/080715123

B. Z. Guo, Riesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1736-1747, 2001.
DOI : 10.1137/S0363012999354880

B. Z. Guo, Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients, SIAM Journal on Control and Optimization, vol.40, issue.6, pp.1905-1923, 2002.
DOI : 10.1137/S0363012900372519

B. Z. Guo and X. Zhang, The Regularity of the Wave Equation with Partial Dirichlet Control and Colocated Observation, SIAM Journal on Control and Optimization, vol.44, issue.5, pp.1598-1613, 2005.
DOI : 10.1137/040610702

B. Z. Guo and Z. C. Shao, Regularity of a Schr??dinger equation with Dirichlet control and colocated observation, Systems & Control Letters, vol.54, issue.11, pp.1135-1142, 2005.
DOI : 10.1016/j.sysconle.2005.04.008

M. Hautus, Controllability and observability conditions of linear autonomous systems, Proc., Ser. A, pp.443-448, 1969.

F. L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Diff. Eqns, vol.1, pp.45-53, 1985.

L. Josserand, Commande frontière par modèle interne de systèmes à paramètres distribués . Application à un double échangeur de chaleur, Thèse de Doctorat, 1996.

V. Jurdjevic and J. P. Quinn, Controllability and stability, Journal of Differential Equations, vol.28, issue.3, pp.381-389, 1978.
DOI : 10.1016/0022-0396(78)90135-3

R. E. Kalman, Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana, vol.5, pp.102-119, 1960.

R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

T. Kato, Pertubation Theory for Linear Operators, 1966.

V. Komornik, Exact Controllability and Stabilization : The Multiplier Method, 1994.

P. S. Krishnaprasad and J. E. Marsden, Hamiltonian structures and stability for rigid bodies with flexible attachments. Rational Mechanics and Analysis, pp.98-171, 1987.

H. Laousy, C. Z. Xu, and G. Sallet, Boundary feedback stabilization of a rotating body-beam system, IEEE Transactions on Automatic Control, vol.41, issue.2, pp.241-245, 1996.
DOI : 10.1109/9.481526

B. Laroche, P. Martin, and P. Rouchon, Motion planning for the heat equation, International Journal of Robust and Nonlinear Control, vol.59, issue.60, pp.629-643, 2000.
DOI : 10.1002/1099-1239(20000715)10:8<629::AID-RNC502>3.0.CO;2-N

I. Lasiecka, Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary, Journal of Differential Equations, vol.79, issue.2, pp.340-381, 1989.
DOI : 10.1016/0022-0396(89)90107-1

I. Lasiecka and R. Triggiani, L2(??)-regularity of the boundary to boundary operator B???L for hyperbolic and Petrowski PDEs, Abstract and Applied Analysis, vol.2003, issue.19, pp.1061-1139, 2003.
DOI : 10.1155/S1085337503305032

A. and L. Pourhiet, Résolution Numérique des Equations aux Dérivées Partielles, Cépaduès-Editions, 1988.

K. Lenz, H. Özbay, A. Tannenbaum, J. Turi, and B. Morton, Frequency domain analysis and robust control design for an ideal flexible beam, Automatica, vol.27, issue.6, pp.947-961, 1991.
DOI : 10.1016/0005-1098(91)90130-T

L. Léon and E. Zuazua, Boundary controllability of the finite-difference space semi-discretizations of the beam equation, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.827-862, 2002.
DOI : 10.1051/cocv:2002025

X. D. Li, C. Z. Xu, Y. J. Peng, and M. Tucsnak, On the numerical investigation of a Luenberger type observer for infinite-dimensional vibrating systems, 17 th IFAC World Congress, 2008.
DOI : 10.3182/20080706-5-KR-1001.01289

URL : https://hal.archives-ouvertes.fr/hal-00457879

X. D. Li, C. Z. Xu, Y. J. Peng, and M. Tucsnak, Etude numérique sur un observateur du type Luenberger pour des systèmes de vibration en dimension infinie. 3 ` emes Journées Doctorales, Journées Nationales MACS, 2009.

X. D. Li and C. Z. Xu, A further numerical investigation on Luenberger type observers for vibrating systems, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009.
DOI : 10.1109/CDC.2009.5400041

URL : https://hal.archives-ouvertes.fr/hal-00647261

X. D. Li and C. Z. Xu, Infinite-dimensional Luenberger-like observers for a rotating bodybeam system, Syst. Contr. Lett
URL : https://hal.archives-ouvertes.fr/hal-00647239

J. Liéto, Le Génie Chimique à l'Usage des Chimistes, Lavoisier TEC & DOC, 1998.

J. L. Lions, Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Recherches en Mathématiques Appliquées, 1988.

K. Liu, Z. Liu, and B. Rao, Exponential Stability of an Abstract Nondissipative Linear System, SIAM Journal on Control and Optimization, vol.40, issue.1, pp.149-165, 2001.
DOI : 10.1137/S0363012999364930

URL : https://hal.archives-ouvertes.fr/hal-00129638

C. Lobry, Bases Mathématiques de la Théorie des Systèmes Asservis Non Linéaires, Analyse Appliquée et Informatique, 1976.

D. G. Luenberger, Observers for multivariable systems, IEEE Transactions on Automatic Control, vol.11, issue.2, pp.190-197, 1966.
DOI : 10.1109/TAC.1966.1098323

Z. H. Luo, B. Z. Guo, and O. Mörgul, Stability and Stabilization of In5nite Dimensional Systems with Applications, 1999.

P. Martin and P. Rouchon, Systèmes différentiellement plats. Notes de cours, Journées XUPS, 1999.

T. D. Nguyen and O. Egeland, Tracking and observer design for a motorized Euler-Bernoulli beam, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.3325-3330, 2003.
DOI : 10.1109/CDC.2003.1271657

T. D. Nguyen and O. Egeland, Observer design for a towed seismic cable, Proc. American Control Conference, pp.2233-2238, 2004.

U. Nieken, G. Kolios, and G. Eigenberger, Limiting cases and approximate solutions for fixed-bed reactors with periodic flow reversal, AIChE Journal, vol.41, issue.8, pp.41-49, 1995.
DOI : 10.1002/aic.690410809

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1983.
DOI : 10.1007/978-1-4612-5561-1

K. Phung and X. Zhang, Time Reversal Focusing of the Initial State for Kirchhoff Plate, SIAM Journal on Applied Mathematics, vol.68, issue.6, pp.1535-1556, 2008.
DOI : 10.1137/070684823

S. Pohjolainen and I. Lätti, Robust controller for boundary control systems, International Journal of Control, vol.38, issue.6, pp.1189-1197, 1983.
DOI : 10.1080/00207178308933139

M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, 1984.
DOI : 10.1007/978-1-4612-5282-5

K. Ramdani, T. Takahashi, G. Tenenbaum, and M. Tucsnak, A spectral approach for the exact observability of infinite-dimensional systems with skew-adjoint generator, Journal of Functional Analysis, vol.226, issue.1, pp.193-229, 2005.
DOI : 10.1016/j.jfa.2005.02.009

URL : https://hal.archives-ouvertes.fr/hal-00091371

K. Ramdani, M. Tucsnak, and G. Weiss, Recovering the initial state of an infinitedimensional system using observers, Automatica
URL : https://hal.archives-ouvertes.fr/hal-00529834

B. P. Rao, Le taux optimal de d??croissance de l'??nergie dans l'??quation de poutre de Rayleigh, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.325, issue.7, pp.737-742, 1997.
DOI : 10.1016/S0764-4442(97)80051-1

J. Rauch and M. Taylor, Exponential Decay of Solutions to Hyperbolic Equations in Bounded Domains, Indiana University Mathematics Journal, vol.24, issue.1, pp.79-86, 1974.
DOI : 10.1512/iumj.1975.24.24004

R. Rebarber and G. Weiss, Necessary conditions for exact controllability with a finite-dimensional input space, Systems & Control Letters, vol.40, issue.3, pp.217-227, 2000.
DOI : 10.1016/S0167-6911(00)00029-3

M. Renardy, On the linear stability of hyperbolic PDEs and viscoelastic flows, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.23, issue.6, pp.854-865, 1994.
DOI : 10.1007/BF00952081

J. Rudolph, Flatness Based Control of Distributed Parameter Systems, 2003.

D. L. Russell, Distributed parameter systems : an overview. Encyclopedia of LIFE Support on Control Systems, Robotics and Automation I, pp.933-979, 2002.

F. Simondon and H. Touré, A Lyapunov functional and long-time behaviour for a degenerate parabolic problem, Advances in Mathematical Sciences and Applications, pp.6-1243, 1996.

M. Slemrod, A Note on Complete Controllability and Stabilizability for Linear Control Systems in Hilbert Space, SIAM Journal on Control, vol.12, issue.3, pp.500-508, 1974.
DOI : 10.1137/0312038

E. D. Sontag, Mathematical Control Theory : Deterministic Finite Dimensional Systems, 1990.

O. J. Staffans and G. Weiss, Transfer functions of regular linear systems Part II : The System Operator and the Lax-Phillips Semigroup, 2000.

G. Strange and G. Fix, An Analysis of the Finite-Element Method, Journal of Applied Mechanics, vol.41, issue.1, 1973.
DOI : 10.1115/1.3423272

A. Tchousso, Étude de la stabilité asymptotique de quelques modèles de transfert de chaleur, Thèse de Doctorat, 2004.

A. Tchousso, X. D. Li, C. Z. Xu, and G. Sallet, Stabilité L p exponentielle d'un réseau d'échangeurs thermiques avec diffusion et sans diffusion, 2009.

H. Touré, Etude des équations générales u t ? ?(u) xx + f (u) x = v par la théorie des semi-groupes non linéaires dans L 1, Thèse de Doctorat, 1982.

R. Triggiani, On the stabilizability problem in Banach space, Journal of Mathematical Analysis and Applications, vol.52, issue.3, pp.383-403, 1975.
DOI : 10.1016/0022-247X(75)90067-0

M. Tucsnak and G. Weiss, Simultaneous Exact Controllability and Some Applications, SIAM Journal on Control and Optimization, vol.38, issue.5, pp.1408-1427, 2000.
DOI : 10.1137/S0363012999352716

M. Tucsnak and G. Weiss, Observation and control for operator semigroups. Birkhäuser Advanced Texts, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00590673

D. Vortmeyer and R. J. Schaefer, Equivalence of one- and two-phase models for heat transfer processes in packed beds: one dimensional theory, Chemical Engineering Science, vol.29, issue.2, pp.485-491, 1974.
DOI : 10.1016/0009-2509(74)80059-X

G. Weiss, Admissible observation operators for linear semigroups, Israel Journal of Mathematics, vol.15, issue.1, pp.17-43, 1989.
DOI : 10.1007/BF02788172

G. Weiss, Regular linear systems with feedback, Mathematics of Control, Signals, and Systems, vol.342, issue.1, pp.23-57, 1994.
DOI : 10.1007/BF01211484

G. Weiss, Transfer Functions of Regular Linear Systems. Part I: Characterizations of Regularity, Transactions of the American Mathematical Society, vol.342, issue.2, pp.827-854, 1994.
DOI : 10.2307/2154655

G. Weiss and R. F. Curtain, Exponential stabilization of vibrating systems by collocated feedback, Proc. 7th IEEE Mediterranean Symposium on Control and Automation, 1999.

G. Weiss and R. F. Curtain, Exponential stabilization of a Rayleigh beam using colocated control, IEEE Trans. Auto. Control, pp.53-3643, 2008.

C. Z. Xu, Quelques résultats concrets sur la commande linéaire par l'approche H ?, Thèse de Doctorat, 1989.

C. Z. Xu, Commande des systèmes à paramètres distribués. Mémoire de l'Habilitation à Diriger la Recherche, 1997.

C. Z. Xu and J. Baillieul, Stabilizability and stabilization of a rotating body-beam system with torque control, IEEE Transactions on Automatic Control, vol.38, issue.12, pp.1754-1765, 1993.
DOI : 10.1109/9.250555

C. Z. Xu and J. P. Gauthier, Analyse et commande d'un échangeur thermique à contrecourant, RAIRO APPII, vol.25, pp.377-396, 1991.

C. Z. Xu, J. P. Gauthier, and I. Kupka, Exponential stability of the heat exchanger equation, Proc. European Control Conference, pp.303-307, 1993.

C. Z. Xu, P. Ligarius, and J. P. Gauthier, An observer for infinite-dimensional dissipative bilinear systems, Computers & Mathematics with Applications, vol.29, issue.7, pp.13-21, 1995.
DOI : 10.1016/0898-1221(95)00014-P

C. Z. Xu and G. Sallet, Boundary stabilization of rotating flexible systems, Lectures Notes in Control and Information Sciences, vol.185, pp.347-365, 1992.
DOI : 10.1007/BFb0115035

C. Z. Xu and G. Sallet, Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems, ESAIM: Control, Optimisation and Calculus of Variations, vol.7, pp.421-442, 2002.
DOI : 10.1051/cocv:2002062

C. Z. Xu and G. Weiss, Spectral properties of infinite-dimensional closed-loop systems, Mathematics of Control, Signals and Systems, vol.17, pp.153-172, 2005.

K. Yosida, Functional Analysis, 1995.

T. I. Zelenyak, Stabilisation of solutions of boundary value problems for a second order parabolic equation with one space variable, Differentsial'nye Uralvneniya, pp.34-3517, 1968.