D. Santos, M. V. Rodrigues-m, . Wu-y, . Dos-santos-martins-v, . Rodrigues-m et al., Design of a PI Control using Operator Theory for Infinite Dimensional Hyperbolic Systems TCST-2013-0381A Multi- Models approach of Saint-Venant's equations : a stability study by LMI, Publications Internationales avec comité de lecture ? 11 Articles de journal : [TCST-2013], pp.2024-2030

[. , D. Santos-martins-v, C. F. Maschke-b, and J. C. , Méthodes numériques et applications des systèmes à paramètres repartis, Journal Européen des Systèmes Automatisés (JESA), vol.45, pp.665-691665, 2011.

S. B. Dos, S. V. Legorrec-y, M. B. Dos-santos-v, P. C. Dos-santos-v, and . Bastin-g, Volume : 54 Issue :10 A potential link between passivity condition and stability : application on shallow water equations AIMS Networks and Heterogeneous Media (NHM, IF : 0.952Boundary control of open channels with numerical and experimental validationsBoundary control with integral action for hyperbolic systems of conservation laws : Lyapunov stability analysis and experimental validation, Some Properties of Contact Structure Dynamical Systems, pp.2341-2351, 2008.

D. V. Santos, T. Y. Bastin-g, . Dos-santos-v, C. N. Touré-y, . Dos-santos-v et al., Regulation in Multireach Open Channels by Internal Model Boundary Control Special Issue on : Control Applications of Optimisation -control and aeronautics, optimal control, control of partial differential equationsRégulation de Canaux d'irrigation : Approche par Contrôle Frontière Multivariable, et Modèle Interne d'EDP", revue e-STA, Sciences et Technologies de l'AutomatiqueOn the regulation of irrigation canals : multivariable boundary control approach by internal model, IJTS IF : 0.23), pp.91-96, 2004.

C. S. Buet-c, S. V. Dos, F. Taylor, . Santos-martins-v, A. S. Wu-y et al., Using the Hamiltonian Formulation The Netherlands (session invitée) [ECC-2013LMI & BMI Technics for the Design of a PI Control for Irrigation ChannelsControl of a system a coupled PDEs with ODE in infinite dimension ; Application to an extrusion process The Institut Henri Poincaré, HYKE 2003-021 ? 22 Congrès Internationaux avec comités de lecture et actes publiésLink between Dissipativity Expressed in Riemann Coordinates and the Small Gain Theorem The 21st International Symposium on Mathematical Theory of Networks and Systems European Control Conference IFAC CPDE 2013, invited session "PDE Applications" organized by V. Dos Santos Martins, 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations Conférence Internationale Francophone d'Automatique Conférence IEEE, p.2012, 2012.

[. Santos-martins-v and . Rodrigues-m, A Proportional Integral Feedback for Open Channels Control through LMI Design, 18th IFAC World Congress, 2011.

D. M. , D. Santos-martins-v, and C. F. Maschke-b, Well posedness of the model of an extruder in infinite dimension, Liste complète des contributions scientifiques 50th IEEE Conference on Decision and Control and European, Control Conference, 1926.

D. M. Dos, S. V. , R. V. Santos, M. B. Legorrec-y, D. A. Favache et al., Hamiltonian approach to the stabilization of systems of two conservation lawsStability Properties of Contact Structure Dynamical SystemsStructure de jonction pour les systèmes à paramètres distribués : cas des systèmes réversibles et irréversibles", CIFA 2008, n o T18-I-07-0149Approche géométrique pour l'analyse et la commande des systèmes de dimension infinie", CIFA 2008, n o T10-I-41-0239Passivity condition for stability : application on shallow water equationsIrrigation Channels and Related Problems Boundary control of Systems of Conservation Laws : Lyapunov Stability with Integral ActionsBoundary Control of a channel : practical and numerical studiesBoundary Control of a channel :last improvements " ICINCORegulation in Multireach Open Channels by Internal Model Boundary ControlInternal Model Boundary Control of Hyperbolic system : Application to the Regulation of ChannelsMultivariable Boundary Control Approach by Internal Model, applied to Irrigation Canals RegulationIrrigation Multireaches Regulation problem by Internal Model Boundary Control, Une approche Multimodèles des équations de Saint-Venant : une analyse de la stabilité par techniques LMI Conférence Internationale Francophone d'Automatique Conférence IEEE 8th IFAC Symposium on Nonlinear Control Systems European Control Conference 7th IFAC Symposium on Nonlinear Control Systems 3rd IFAC Symposium on System, Structure and Control, SSSC 2007 13th IFAC Workshop on Control Applications of Optimisation, CAO'06 7thPortuguese Conference on Automatic Control -CONTROLO'2006 16th IFAC World Congress'05 Conférence Internationale Francophone d'Automatique Conférence IEEE, pp.2010-2010, 2004.

[. V. Santos and . Touré-y, MULTIVARIABLE BOUNDARY CONTROL APPROACH BY INTERNAL MODEL, APPLIED TO IRRIGATION CANALS REGULATION, Second IFAC Conference on Control Systems Design (CSD'03), pp.56-91, 2003.
DOI : 10.3182/20050703-6-CZ-1902.02101
URL : https://hal.archives-ouvertes.fr/hal-00195122

S. V. Dos and . Touré-y, On the Regulation of Irrigation Canals : Internal Model and Boundary Control Approach, Second International Conference on Signals, Decision and Information Technology (SSD'03), 2003.

D. V. Santos, M. B. Legorrec-y, . Dos-santos-v, S. J. Toure-y, S. V. Dos et al., A Hamiltonian approach to the stabilization of systems of two conservation laws Control of Distributed Parameter SystemsBoundary control of a channel : Internal Model Boundary ControlBoundary control of a channel in presence of small perturbations : a Riemann approach, Publications et Communications sans comité de lecture ? 3 publications internationales, pp.20-24, 2007.

D. V. Santos, Régulation de canaux d'irrigation : contrôle en temps réel d'Equations aux Dérivées Partielles hyperboliques

D. V. Santos, . Rodrigues-m, . Wu-y, R. M. Dos-santos-v, S. V. Dos et al., Design of a PI Control using Operator Theory for Infinite Dimensional Systems : Application to Hyperbolic PDEUne approche Multi-Modèles sur un système hyperbolique en dimension infinieFormulation Hamiltonienne pour la stabilisation de systèmes de lois de conservation non linéaires de dimension infinie : généralisation", séminaire Easy-Commande, INSARégulation de canaux d'irrigation : contrôle en temps réel d'Equations aux Dérivées Partielles hyperboliques, Liste complète des contributions scientifiques Numérique ? 22 séminaires dont 5 invités Groupe de travail Systèmes à Retards, Réunion commune EDP-SAR du 18-19 Septembre 2012. [EDP-2012]Lieu d'Evans : Outils de Synthèse de Contrôle en Dimension Infinie, 2005.

N. I. Akhiezer and I. M. Glazman, with Nestell, Merynd, trans Theory of linear operators in Hilbert space, pp.7-116, 1963.

A. Moghadam, A. Aksikas, I. Dubljevic, S. Forbes, and J. , LQR control of an infinite dimensional time-varying CSTR-PFR system*, 18th IFAC World Congress, 2011.
DOI : 10.3182/20110828-6-IT-1002.02195

B. Andréa-novel, G. Bastin, J. Coron, and J. De-halleux, On boundary control design for quasilinear hyperbolic systems with entropies as Lyapunov functions, Proceedings 41th IEEE Conference on Decision and Control, pp.3010-3014, 2002.

B. Andréa-novel, J. Coron, and G. Bastin, Dissipative boundary conditions for onedimensional nonlinear hyperbolic systems, SIAM J. Control Optim, vol.47, pp.1460-1498, 2008.

G. Bastin and J. , Coron and B. d'Andréa-Novel, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, 43rd IEEE Conference on Decision and Control, 2004.

B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control, Communications and Control Engineering Series ISBN, vol.10, pp.1-84628, 2007.
DOI : 10.1007/978-1-84628-517-2
URL : https://hal.archives-ouvertes.fr/hal-01338369

S. Amin, M. Falk, A. M. Hante, and . Bayen, Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems, IEEE Transactions on Automatic Control, vol.57, issue.2, 2012.
DOI : 10.1109/TAC.2011.2158171

A. Bhagwat, R. Srinivasan, and P. Krishnaswamy, Multi-linear model-based fault detection during process transitions, Chemical Engineering Science, vol.58, issue.9, pp.1649-1670, 2003.
DOI : 10.1016/S0009-2509(03)00008-3

S. Boyd, E. Ghaoui, L. Feron, E. Balakrishnan, and V. , Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, 1994.
DOI : 10.1137/1.9781611970777

S. Choulak, F. Couenne, Y. L. Gorrec, C. Jallut, P. Cassagnau et al., Generic Dynamic Model for Simulation and Control of Reactive Extrusion, Industrial & Engineering Chemistry Research, vol.43, issue.23, pp.43-7373, 2004.
DOI : 10.1021/ie0342964

J. M. Coron and B. , Andréa Novel and G. Bastin, A Lyapunov approach to control irrigation canals modeled by Saint Venant equations, Paper F1008-5 in Proceedings ECC 99, 1999.

J. M. Coron, B. Novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.2-11, 2007.
DOI : 10.1109/TAC.2006.887903

J. Coron, G. Bastin, and B. Andréa-novel, Dissipative Boundary Conditions for One-Dimensional Nonlinear Hyperbolic Systems, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1460-1498, 2008.
DOI : 10.1137/070706847
URL : https://hal.archives-ouvertes.fr/hal-00923596

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

S. Dashkovskiy and A. Mironchenko, Input-to-state stability of infinite-dimensional control systems, Mathematics of Control, Signals, and Systems, pp.1-35, 2013.
DOI : 10.1007/s00498-012-0090-2

A. De-saint-venant, Théorie du mouvement non permanent des eaux avec applications aux crues des rivières et à l'introduction des marées dans leur litComptes rendus de l'Académie des Sciences de Paris, pp.148-154, 1871.

M. Diagne, V. Dos-santos-martins, F. Couenne, B. Maschke, and C. Jallut, Modélisation et commande d'un système d'équations aux dérivées partielles à frontière mobile : application au procédé d'extrusion, JESA, vol.7, pp.45-665

M. Diagne, D. Santos-martins, V. Rodrigues, and M. , Une approche Multi-modèles des équations de Saint-Venant : une analyse de la stabilité par techniques LMIConférence Internationale Francophone d'Automatique, Conférence IEEE, 2010.

M. Diagne, V. Dos-santos-martins, F. Couenne, and B. Maschke, Well posedness of the model of an extruder in infinite dimension, IEEE Conference on Decision and Control and European Control Conference, 1926.
DOI : 10.1109/CDC.2011.6161288

D. Santos, V. Toure, Y. Mendes, E. Courtial, and E. , MULTIVARIABLE BOUNDARY CONTROL APPROACH BY INTERNAL MODEL, APPLIED TO IRRIGATION CANALS REGULATION, 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.02101
URL : https://hal.archives-ouvertes.fr/hal-00195122

D. Santos, V. Bastin, G. Coron, and J. M. , Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments, Automatica, vol.44, issue.5, pp.1310-1318, 2008.
DOI : 10.1016/j.automatica.2007.09.022

D. Santos, V. Prieur, and C. , Boundary Control of Open Channels With Numerical and Experimental Validations, IEEE Transactions on Control Systems Technology, vol.16, issue.6, pp.1252-1264, 2008.
DOI : 10.1109/TCST.2008.919418

V. , D. Santos, B. Maschke, and Y. L. Gorrec, A Hamiltonian perspective to the stabilization of systems of two conservation laws, Networks and Heterogeneous Media (NHM), AIMS, pp.249-266, 2009.
DOI : 10.3934/nhm.2009.4.249

D. Santos-martins, V. Rodrigues, and M. , A Proportional Integral Feedback for Open Channels Control trough LMI Design, 18th IFAC World Congress, 2011.
DOI : 10.3182/20110828-6-IT-1002.01037

D. Santos-martins, V. Diagne, M. Couenne, F. Maschke, and B. , Stabilité d'un procédé d'extrusion par deux systèmes d'équations d'évolution couplés par une interface mobile, pp.4-6, 2012.

D. Santos-martins, V. Rodrigues, M. Diagne, and M. , A Multi-Models Approach of Saint-Venant's Equations : A Stability study LMI, Int. Jour. of Applied Mathematics and Computer Science, vol.22, issue.3, 2012.

D. Santos-martins, V. Wu, Y. Aberkane, S. Rodrigues, and M. Bmi, Technics for the Design of a PI Control for Irrigation Channels, European Control Conference, 2013.

D. Santos-martins and V. , Introduction of a non constant viscosity on an extrusion process, CPDE, "IFAC Workshop on Control of Systems Modeled by Partial Differential Equations, 2013.

D. Santos-martins, V. Rodrigues, M. Wu, and Y. , Design of a Proportional Integral Control Using Operator Theory for Infinite Dimensional Hyperbolic Systems, IEEE Transactions on Control Systems Technology, vol.22, issue.5, pp.2024-2030, 2014.
DOI : 10.1109/TCST.2014.2299407

V. and D. Santos, Link between dissipativity expressed in Riemann coordinates and the Small Gain Theorem, using the Hamiltonian formulation, 2014.

J. F. Dulhoste, G. Besançon, and D. Georges, Nonlinear control of water flow dynamics by input-output linearisation based on a collocation modelEuropean control conf, 2001.

H. O. Fattorini, Boundary Control Systems, SIAM Journal on Control, vol.6, issue.3, 1968.
DOI : 10.1137/0306025

A. Favache, S. Martins, V. Dochain, D. Maschke, and B. , Some Properties of Contact Structure Dynamical Systems, IEEE Transactions on Automatic ControlIEEE TAC, vol.167, issue.3, pp.5410-2341, 2009.

E. Gatzke and F. Doyle, Use of multiple models and qualitative knowledge for on-line moving horizon disturbance estimation and fault diagnosis, Journal of Process Control, vol.12, issue.2, pp.339-352, 2002.
DOI : 10.1016/S0959-1524(01)00037-3

D. Georges and X. Litrico, Automatique pour la Gestion des Ressources en Eau, IC2, Systèmes automatisés, 2002.

J. M. Greenberg and T. Li, The effect of boundary damping for the quasilinear wave equation, Journal of Differential Equations, vol.52, issue.1, pp.66-75, 1984.
DOI : 10.1016/0022-0396(84)90135-9

H. Hamroun, L. Lefevre, and E. Mendes, Port-Based modelling for open channel irrigation systems, WSEAS "Transactions on Applied and Theoretical Mechanics, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00227524

L. P. Janssen, P. F. Rozendal, H. W. Hoogstraten, and M. C. , A Dynamic Model for Multiple Steady States in Reactive Extrusion, International Polymer Processing, vol.16, issue.3, pp.263-271, 2001.
DOI : 10.3139/217.1651

L. P. Janssen, P. F. Rozendal, H. W. Hoogstraten, and M. C. , A Dynamic Model Accounting for Oscillating Behavior in Reactive Extrusion, International Polymer Processing, vol.18, issue.3, pp.277-284, 2003.
DOI : 10.3139/217.1748

T. Kato, Pertubation Theory for Linear Operators, 1976.

A. Khalifeh and J. R. Clermont, Simulations numériques tridimensionnelles d'écoulements non-isothermes dans une extrudeuse monovis (système vis-fourreau) par une méthode de volumes finis, 18ème Congrès Français de Mécanique, pp.2007-1321, 2007.

E. K. Kim and J. L. White, Isothermal transient startup for starved flow modular corotating twin screw extruder, Polymer Engineering and Science A, issue.3, pp.40-543, 2000.

E. K. Kim and J. L. White, Non-Isothermal Transient Startup of A Starved Flow Modular Co-Rotating Twin Screw Extruder, International Polymer Processing, vol.15, issue.3, pp.233-241, 2000.
DOI : 10.3139/217.1596

M. Kulshreshtha, C. Zaror, J. , and D. , Simulating the performance of a control system for food extruders using model-based set-point adjustment, Food Control, vol.6, issue.3, pp.135-141, 1995.
DOI : 10.1016/0956-7135(94)00006-Y

M. Kulshrestha and C. Zaror, An unsteady state model for twin screw extruders, PartC, vol.70, pp.21-28, 1992.

P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, 1973.

Y. , L. Gorrec, H. Zwart, and B. M. Maschke, Dirac structures and boundary control systems associated with skew-symmetric differential operators, SIAM J. of Control and Optimization, vol.44, pp.1864-1892, 2005.

D. J. Leith and W. Leithead, Survey of gain-scheduling analysis and design, International Journal of Control, vol.73, issue.11, pp.1001-1025, 2000.
DOI : 10.1080/002071700411304

T. Li, Global classical solutions for a class of quasilinear hyperbolic systems, Applicable Analysis, vol.28, issue.3-4, 1994.
DOI : 10.1080/00036810108840968

X. Litrico and V. Fromion, H/sub /spl infin// control of an irrigation canal pool with a mixed control politics, IEEE Transactions on Control Systems Technology, vol.14, issue.1, pp.99-101, 2006.
DOI : 10.1109/TCST.2005.860526

X. Litrico and D. Georges, Robust continuous-time and discrete-time flow control of a dam???river system. (I) Modelling, Applied Mathematical Modelling, vol.23, issue.11, pp.809-827, 1999.
DOI : 10.1016/S0307-904X(99)00014-1

C. H. Li, Modelling extrusion cookingMathematical and Computer Modelling, pp.553-563, 2001.

Z. H. Luo, B. Z. Guo, and O. Morgul, Stability and Stabilization of Infinite Dimensional Systems with Applications, Communications and Control Engineering Series, 1999.
DOI : 10.1007/978-1-4471-0419-3

A. Macchelli and C. Melchiorri, Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.743-767, 2004.
DOI : 10.1137/S0363012903429530

P. O. Malaterre, D. Rogers, and J. Schuurmans, Classification of Canal Control Algorithms, Journal of Irrigation and Drainage Engineering, vol.124, issue.1, pp.3-10, 1998.
DOI : 10.1061/(ASCE)0733-9437(1998)124:1(3)

I. Mareels, E. Weyer, S. Ooi, M. Cantoni, Y. Li et al., Systems engineering for irrigation systems: Successes and challenges, Annual Reviews in Control, vol.29, issue.2, pp.191-204, 2005.
DOI : 10.1016/j.arcontrol.2005.08.001

B. Maschke, R. Ortega, A. J. Van-der-schaft, and G. Escobar, Interconnection and damping assignment : passivity-based control of port-controlled Hamiltonian systems, Automatica J. IFAC, vol.38, pp.585-596, 2002.

B. Maschke, A. J. Van, and . Schaft, 4 Compositional Modelling of Distributed-Parameter Systems, Lecture Notes in Control and Information Sciences, vol.311, pp.115-154, 2004.
DOI : 10.1007/11334774_4

F. Mazenc and C. Prieur, Strict Lyapunov functions for semilinear parabolic partial differential equations, Mathematical Control and Related Fields, vol.1, issue.2, pp.231-250, 2011.
DOI : 10.3934/mcrf.2011.1.231
URL : https://hal.archives-ouvertes.fr/hal-00599068

R. Murray-smith and T. Johansen, Multiple Model Approaches to Modelling and Control, 1997.

R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-ramirez, Passivity-based control of Euler-Lagrange Systems, Communications and Control Series, 1998.
DOI : 10.1007/978-1-4471-3603-3

R. Ortega, A. J. Van-der-schaft, I. Mareels, and B. Maschke, Putting energy back in control, IEEE Control Systems Magazine, vol.21, issue.2, pp.18-32, 2001.
DOI : 10.1109/37.915398

M. Papageorgiou and A. Messmer, Flow control of a long river stretch, Automatica, vol.25, issue.2, pp.177-183, 1989.
DOI : 10.1016/0005-1098(89)90071-X

R. Pasumarthy, A. J. Van, and . Schaft, A port-Hamiltonian approach on modeling and interconnections of canal systems, Proceeding of the Mathematical Theory of Networks and Systems Conference, p.6, 2006.

S. Pohjolainen, Robust multivariable PI-controller for infinite dimensional systems, IEEE Transactions on Automatic Control, vol.27, issue.1, pp.17-30, 1982.
DOI : 10.1109/TAC.1982.1102887

M. Rodrigues, M. Sahnoun, D. Theilliol, and J. Ponsart, Sensor fault detection and isolation filter for polytopic LPV systems: A winding machine application, Journal of Process Control, vol.23, issue.6, pp.805-816, 2013.
DOI : 10.1016/j.jprocont.2013.04.002
URL : https://hal.archives-ouvertes.fr/hal-00823560

M. Rodrigues, Y. Wu, S. Aberkane, D. Santos-martins, and V. , LMI & BMI Technics for the Design of a PI Control for Irrigation Channels, ECC 2013, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00823551

M. Rodrigues, D. Theilliol, S. Aberkane, and D. Sauter, Fault Tolerant Control Design For Polytopic LPV Systems, International Journal of Applied Mathematics and Computer Science, vol.17, issue.1, pp.27-37, 2007.
DOI : 10.2478/v10006-007-0004-5
URL : https://hal.archives-ouvertes.fr/hal-00095582

A. Sasane and R. F. Curtain, Optimal Hankel norm approximation for the Pritchard-Salamon class of infinite-dimensional systems, Integral Equations and Operator Theory, vol.25, issue.2, pp.98-126, 2001.
DOI : 10.1007/BF01192150

R. Skelton, T. Iwasak, and K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, 1997.

Y. Touré and R. J. , Controller design for distributed parameter systemsEncyclopedia of LIFE Support on Control Systems, Robotics and Automation, pp.933-979, 2002.

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

A. J. Van and . Schaft, Springer Communications and Control Engineering series, Passivity Techniques in Nonlinear Control, 2000.

A. J. Van-der-schaft and B. M. Maschke, Hamiltonian formulation of distributed-parameter systems with boundary energy flow, Journal of Geometry and Physics, vol.42, issue.1-2, pp.166-194, 2002.
DOI : 10.1016/S0393-0440(01)00083-3

B. Vergnes and F. Berzin, Modeling of??reactive systems in??twin-screw extrusion: challenges and??applications, Comptes Rendus Chimie, vol.9, issue.11-12, pp.11-12, 2006.
DOI : 10.1016/j.crci.2006.07.006
URL : https://hal.archives-ouvertes.fr/hal-00510653

J. A. Villegas, H. Zwart, Y. L. Gorrec, and B. Maschke, Stability and Stabilization of a Class of Boundary Control Systems, Proceedings of the 44th IEEE Conference on Decision and Control, 2005.
DOI : 10.1109/CDC.2005.1582762

J. A. Villegas, A Port-Hamiltonian Approach to Distributed Parameter Systems, 2007.

J. A. Villegas, Y. Le-gorrec, H. Zwart, and B. Maschke, Boundary control for a class of dissipative differential operators including diffusion systems, Proc. 7th International Symposium on Mathematical Theory of Networks and Systems, pp.297-304, 2006.

Y. Wang and J. Tan, Dual-target predictive control and application in food extrusion, Control Engineering Practice, vol.8, issue.9, pp.1055-1062, 2000.
DOI : 10.1016/S0967-0661(00)00025-3

E. Weyer, Decentralised PI controller of an open water channel, 15th IFAC world congress, 2002.

J. C. Willems, Dissipative dynamical systems part I: General theory, Archive for Rational Mechanics and Analysis, vol.34, issue.No. 4, pp.352-393, 1972.
DOI : 10.1007/BF00276493

L. Zaccarian, Y. Li, E. Weyer, M. Cantoni, and A. Teel, Anti-windup for marginally stable plants and its application to open water channel control systems, Control Engineering Practice, vol.15, issue.2, pp.261-272, 2007.
DOI : 10.1016/j.conengprac.2006.08.001

R. Sepulchre, M. Jankovi´cjankovi´c, and P. Kokotovi´ckokotovi´c, Contructive Nonlinear Control, Communications and Control Engineering, 1997.

A. Moghadam, A. Aksikas, I. Dubljevic, S. Forbes, and J. , LQR control of an infinite dimensional time-varying cstr-pfr system, 18th IFAC World Congress Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems, IEEE Transactions on Automatic Control, vol.57, issue.2, pp.291-301, 2011.

A. Bhagwat, R. Srinivasan, and P. R. Krishnaswamy, Multi-linear model-based fault detection during process transitions, Chemical Engineering Science, vol.58, issue.9, pp.1649-1670, 2003.
DOI : 10.1016/S0009-2509(03)00008-3

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

S. Dashkovskiy and A. Mironchenko, Input-to-state stability of infinite-dimensional control systems, Mathematics of Control, Signals, and Systems, vol.45, issue.641, pp.1-35, 2013.
DOI : 10.1007/s00498-012-0090-2

A. B. De-saint-venant, Théorie du mouvement non permanent des eaux avec applications aux crues desrivì eres etàet`età l'introduction des marées dans leur lit. Comptes rendus de l'Académie des Sciences de Paris 73, pp.148-154

D. Santos, V. Bastin, G. Coron, J. M. Novel, and B. , Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments, Automatica, vol.44, issue.5, pp.1310-1318, 2008.
DOI : 10.1016/j.automatica.2007.09.022

D. Santos, V. Toure, Y. Mendes, E. Courtial, and E. , MULTIVARIABLE BOUNDARY CONTROL APPROACH BY INTERNAL MODEL, APPLIED TO IRRIGATION CANALS REGULATION, Proc. 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.02101
URL : https://hal.archives-ouvertes.fr/hal-00195122

D. Santos-martins, V. Rodrigues, and M. , A Proportional Integral Feedback for Open Channels Control trough LMI Design, 18th IFAC World Congress, 2011.
DOI : 10.3182/20110828-6-IT-1002.01037

D. Santos-martins, V. Rodrigues, M. Diagne, and M. , A Multi-Models Approach of Saint-Venant's Equations: A Stability study LMI, Int. Jour. of Applied Mathematics and Computer Science, vol.22, issue.3, 2012.

J. F. Dulhoste, G. Besançon, and D. Georges, Nonlinear control of water flow dynamics by input-output linearisation based on a collocation model, European control conf, 2001.

J. M. Greenberg and T. Li, The effect of boundary damping for the quasilinear wave equation, Journal of Differential Equations, vol.52, issue.1, pp.66-75, 1984.
DOI : 10.1016/0022-0396(84)90135-9

D. J. Leith and W. E. Leithead, Survey of gain-scheduling analysis and design, International Journal of Control, vol.73, issue.11, pp.1001-1025, 2000.
DOI : 10.1080/002071700411304

T. Li, Global classical solutions for a class of quasilinear hyperbolic systems, Applicable Analysis, vol.28, issue.3-4, 1994.
DOI : 10.1080/00036810108840968

X. Litrico and D. Georges, Robust continuous-time and discrete-time flow control of a dam???river system. (II) Controller design, Applied Mathematical Modelling, vol.23, issue.11, pp.809-827, 1999.
DOI : 10.1016/S0307-904X(99)00013-X

R. Murray-smith and T. Johansen, Multiple Model Approaches to Modelling and Control, 1997.

M. Papageorgiou and A. Messmer, Flow control of a long river stretch, Automatica, vol.25, issue.2, pp.177-183, 1989.
DOI : 10.1016/0005-1098(89)90071-X

M. Rodrigues, Y. Wu, S. Aberkane, D. Santos-martins, and V. , LMI & BMI Technics for the Design of a PI Control for Irrigation Channels, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00823551

R. Skelton, T. Iwasak, and K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, 1997.

Y. Touré and R. J. , Controller design for distributed parameter systems, Encyclopedia of LIFE Support on Control Systems, Robotics and Automation, pp.933-979, 2002.

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

E. Weyer, Decentralised PI controller of an open water channel, 15th IFAC world congress, 2002.

L. Zaccarian, Y. Li, E. Weyer, M. Cantoni, and A. R. Teel, Anti-windup for marginally stable plants and its application to open water channel control systems, Control Engineering Practice, vol.15, issue.2, pp.261-272, 2007.
DOI : 10.1016/j.conengprac.2006.08.001

S. Aberkane, J. Ponsart, M. Rodrigues, and D. Sauter, Output feedback control of a class of stochastic hybrid systems, Automatica, vol.44, issue.5, pp.1325-1332, 2008.
DOI : 10.1016/j.automatica.2007.09.021
URL : https://hal.archives-ouvertes.fr/hal-00201094

M. Athans, S. Fekri, and A. Pascoal, ISSUES ON ROBUST ADAPTIVE FEEDBACK CONTROL, Proc. 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.01036

M. Chadli, D. Maquin, and J. Ragot, Output stabilisation in multiple model approach to modelling, Proceedings of the International Conference on Control Applications, pp.1315-1320, 2002.
DOI : 10.1109/CCA.2002.1038797
URL : https://hal.archives-ouvertes.fr/hal-00201427

A. B. De-saint-venant, Théorie du mouvement non permanent des eaux avec applications aux crues desrivì eres etàet`età l'introduction des marées dans leur lit, Comptes rendus de l'Académie des Sciences de Paris 73, pp.148-154, 1871.

M. Diagne, D. Santos, V. Rodrigues, and M. , Une approche Multi-modèles deséquationsdeséquations de Saint-Venant : une analyse de la stabilité par techniques LMI, Proc. of 6th IEEE Conférence Internationale Francophone d'Automatique, 2010.

D. Santos and V. , Contrôlefrontì ere par modèle interne de systèmes hyperboliques : ApplicationàApplication`Applicationà la régulation de canaux d'irrigation, 2004.

. Georges, Automatique pour la Gestion des Ressources en Eau, 2002.

J. Greenberg and T. Li, The effect of boundary damping for the quasilinear wave equation, Journal of Differential Equations, vol.52, issue.1, pp.66-75, 1984.
DOI : 10.1016/0022-0396(84)90135-9

D. J. Leith and W. E. Leithead, Survey of gain-scheduling analysis and design, International Journal of Control, vol.73, issue.11, pp.1001-1025, 2000.
DOI : 10.1080/002071700411304

X. Litrico, V. Fromion, J. Baume, C. Arranja, and M. Rijo, Experimental validation of a methodology to control irrigation canals based on Saint-Venant equations, Control Engineering Practice, vol.13, issue.11, pp.1425-1437, 2005.
DOI : 10.1016/j.conengprac.2004.12.010

X. Litrico and D. Georges, Robust continuous-time and discrete-time flow control of a dam???river system. (I) Modelling, Applied Mathematical Modelling, vol.23, issue.11, 1999.
DOI : 10.1016/S0307-904X(99)00014-1

C. Lopez-toribio, R. Patton, and S. Daley, A mutiple-model approach to fault-tolerant control using takagi-sugeno fuzzy modelling: real application to an induction motor drive system, European Control Conference, ECC 99, 1999.

P. Malaterre, Le contrôle automatique des canaux d'irrigation : Etat de l'art et perspectives, Proc. of Colloque Automatique et Agronomie, 2003.

P. Malaterre, D. Rogers, and J. Schuurmans, Classification of Canal Control Algorithms, Journal of Irrigation and Drainage Engineering, vol.124, issue.1, pp.3-10, 1998.
DOI : 10.1061/(ASCE)0733-9437(1998)124:1(3)

R. Murray-smith and T. Johansen, Multiple Model Approaches to Modelling and Control, 1997.

K. Narendra, J. Balakrishnan, and M. Kermal, Adaptation and learning using multiple models, switching, and tuning, IEEE Control Systems Magazine, vol.15, issue.3, pp.37-51, 1995.
DOI : 10.1109/37.387616

C. R. Porfirio, E. A. Neito, and D. Odloak, Multi-model predictive control of an industrial C3/C4 splitter, Control Engineering Practice, vol.11, issue.7, pp.765-779, 2003.
DOI : 10.1016/S0967-0661(02)00183-1

M. Rodrigues, D. Theilliol, M. Adam-medina, and D. Sauter, A fault detection and isolation scheme for industrial systems based on multiple operating models, Control Engineering Practice, vol.16, issue.2, pp.225-239, 2008.
DOI : 10.1016/j.conengprac.2006.02.020
URL : https://hal.archives-ouvertes.fr/hal-00158391

D. Theilliol, D. Sauter, and J. Ponsart, A multiple model based approach for Fault Tolerant Control in nonlinear systems, Proc. IFAC Symposium Safeprocess, 2003.

Y. Toure and L. Josserand, Semigroup formalism and internal model control for a heat exchanger, Revue electronique des sciences et technologies de lautomatique, e-STA, 2004.

E. Weyer, Decentralised pi controller of an open water channel, 15th IFAC world congress, 2002.

D. Santos, M. V. Dos-santos-martins-v, and C. F. , Control of a system a coupled PDEs with ODE in infinite dimension ; Application to an extrusion process", IFAC CPDE 2013, invited session "PDE Applications" organized by V. Dos Santos Martins, 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations The Institut Henri Poincaré, 2013.

B. Vergnes and F. Berzin, Modeling of reactive systems in twinscrew extrusion: challenges and applications, C. R. chimie A, vol.9, pp.11-12, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00510653

E. K. Kim and J. L. White, Isothermal transient startup of a starved flow modular co-rotating twin screw extruder, Polymer Engineering & Science, vol.51, issue.3, pp.543-553, 2000.
DOI : 10.1002/pen.11185

L. P. Janssen, P. F. Rozendal, and M. C. Hoogstraten, A Dynamic Model for Multiple Steady States in Reactive Extrusion, International Polymer Processing, vol.16, issue.3, pp.263-271, 2001.
DOI : 10.3139/217.1651

M. Kulshreshtha, C. Zaror, and D. Jukes, Simulating the performance of a control system for food extruders using model-based set-point adjustment, Food Control, vol.6, issue.3, pp.135-141, 1995.
DOI : 10.1016/0956-7135(94)00006-Y

Y. Wang and J. Tan, Dual-target predictive control and application in food extrusion, Control Engineering Practice, vol.8, issue.9, pp.1055-1062, 2000.
DOI : 10.1016/S0967-0661(00)00025-3

M. Kulshrestha and C. Zaror, An unsteady state model for twin screw extruders, PartC, vol.70, pp.21-28, 1992.

C. Li, Modelling extrusion cooking, Mathematical and Computer Modelling, vol.33, issue.6-7, pp.553-563, 2001.
DOI : 10.1016/S0895-7177(00)00261-2

T. Kato, Pertubation Theory for Linear Operators, 1976.

V. D. Santos, Y. Touré, E. Mendes, and E. Courtial, MULTIVARIABLE BOUNDARY CONTROL APPROACH BY INTERNAL MODEL, APPLIED TO IRRIGATION CANALS REGULATION, Proc. 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.02101
URL : https://hal.archives-ouvertes.fr/hal-00195122

F. Conrad, D. Hilhorst, and T. I. Seidman, Well-posedness of a moving boundary problem arising in a dissolution-growth process, Nonlinear Analysis: Theory, Methods & Applications, vol.15, issue.5, pp.445-465, 1990.
DOI : 10.1016/0362-546X(90)90126-2

B. Boutin, C. Chalons, and P. Raviart, EXISTENCE RESULT FOR THE COUPLING PROBLEM OF TWO SCALAR CONSERVATION LAWS WITH RIEMANN INITIAL DATA, Mathematical Models and Methods in Applied Sciences, vol.20, issue.10, pp.1859-1898, 2010.
DOI : 10.1142/S0218202510004817
URL : https://hal.archives-ouvertes.fr/hal-00871839

M. Diagne, V. D. Santos, F. Couenne, B. Maschke, and C. Jallut, Modélisation et commande d'un système d'´ equations aux dérives partiellesfrontì ere mobile : application au procédé d'extrusion, 2010.

R. Curtain and H. Zwart, An introduction to Infinite Dimensional Linear Systems, ser. Texts in applied Mathematics, 1995.

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, ser, Applied Mathematical Sciences, vol.44, 1983.

D. Santos, M. V. Favache, D. Santos-martins-v, and D. D. Maschke-b, Link between Dissipativity Expressed in Riemann Coordinates and the Small Gain Theorem, Using the Hamiltonian Formulation The Netherlands (session invitée)Some Properties of Contact Structure Dynamical Systems, The 21st International Symposium on Mathematical Theory of Networks and Systems, pp.3-167, 2009.

N. I. Akhiezer and I. M. Glazman, with Nestell, Merynd, trans Theory of linear operators in Hilbert space, pp.7-116, 1963.

B. Andra-novel, G. Bastin, J. Coron, and J. De-halleux, On boundary control design for quasilinear hyperbolic systems with entropies as Lyapunov functions, Proceedings 41th IEEE Conference on Decision and Control, pp.3010-3014, 2002.

J. Andra-novel, G. Coron, and . Bastin, Dissipative boundary conditions for one-dimensional nonlinear hyperbolic systems, SIAM J. Control Optim, pp.47-1460, 2008.

G. Bastin and J. , Coron and B. d'Andra-Novel, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, 43rd IEEE Conference on Decision and Control, 2004.

). B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control, Communications and Control Engineering Series ISBN, vol.10, pp.1-84628, 2007.
DOI : 10.1007/978-1-84628-517-2
URL : https://hal.archives-ouvertes.fr/hal-01338369

J. M. Coron, B. , A. Novel, and G. Bastin, A Lyapunov approach to control irrigation canals modeled by Saint Venant equations, Paper F1008-5 in Proceedings ECC 99, 1999.

). J. Coron, B. , A. Novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Trans. Automat. Control, pp.52-54, 2007.

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

V. D. Santos, G. Bastin, and J. M. , Coron and B. d'Andrea Novel, Boundary control with integral action for hyperbolic systems of conservation laws : Lyapunov stability analysis and experimental validation, Automatica, pp.44-1310, 2008.

V. , D. Santos, and C. Prieur, Boundary control of open channels with numerical and experimental validations, IEEE Transactions on Control Systems Technology, pp.16-1252, 2008.

). Greenberg and T. T. Li, The effect of boundary damping for the quasilinear wave equation, Journal of Differential Equations, vol.52, issue.1, pp.52-66, 1984.
DOI : 10.1016/0022-0396(84)90135-9

). P. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, 1973.

). Y. Le-gorrec, H. Zwart, and B. M. Maschke, Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators, SIAM Journal on Control and Optimization, vol.44, issue.5, pp.44-1864, 2005.
DOI : 10.1137/040611677

). Z. Luo, B. Z. Guo, and O. Morgul, Stability and Stabilization of Infinite Dimensional Systems with Applications, Communications and Control Engineering Series, 1999.
DOI : 10.1007/978-1-4471-0419-3

). A. Macchelli and C. Melchiorri, Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.743-767, 2004.
DOI : 10.1137/S0363012903429530

). B. Maschke, A. J. Van, and . Schaft, 4 Compositional Modelling of Distributed-Parameter Systems, Lecture Notes in Control and Information Sciences, vol.311, pp.115-154, 2004.
DOI : 10.1007/11334774_4

). B. Maschke, R. Ortega, A. J. Van-der-schaft, and G. Escobar, Interconnection and damping assignment: passivity-based control of port-controlled Hamiltonian systems, Automatica J. IFAC, vol.38, pp.585-596, 2002.

R. Ortega, A. J. Van-der-schaft, I. Mareels, and B. Maschke, Putting energy back in control, IEEE Control Systems Magazine, vol.21, issue.2, pp.18-32, 2001.
DOI : 10.1109/37.915398

R. Sepulchre, M. Jankovi´cjankovi´c, and P. Kokotovi´ckokotovi´c, Contructive Nonlinear Control, Communications and Control Engineering, 1997.

A. J. Van and . Schaft, Springer Communications and Control Engineering series, -Gain and Passivity Techniques in Nonlinear Control, pp.3-540, 1996.

O. J. Staffans and G. Weiss, A Physically Motivated Class of Scattering Passive Linear Systems, SIAM Journal on Control and Optimization, vol.50, issue.5, pp.3083-3112, 2012.
DOI : 10.1137/110846403

J. A. Villegas, H. Zwart, Y. L. Gorrec, and B. Maschke, Stability and Stabilization of a Class of Boundary Control Systems, to appear in, IEEE Trans. Automatic Control

J. A. Villegas, A Port-Hamiltonian Approach to Distributed Parameter Systems, 2007.

H. Khalil, Nonlinear Systems, 2002.

A. Van and . Schaft, L2-Gain and Passivity Techniques in Non-Linear Control, ser. Lecture notes in Control and Information Science, 1996.

D. Jeltsema, R. Ortega, and J. M. Scherpen, An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems, Automatica, vol.40, issue.9, pp.1643-1646, 2004.
DOI : 10.1016/j.automatica.2004.04.007

B. Maschke, R. Ortega, A. Van, and . Schaft, Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation, IEEE Transactions on Automatic Control, vol.45, issue.8, pp.1498-1502, 2000.
DOI : 10.1109/9.871758

R. Ortega, A. Van-der-schaft, I. Mareels, and B. Maschke, Putting energy back in control, IEEE Control Systems Magazine, vol.21, issue.2, pp.18-33, 2001.
DOI : 10.1109/37.915398

R. Ortega, A. Van-der-schaft, B. Maschke, and G. Escobar, Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems, Automatica, vol.38, issue.4, pp.585-596, 2002.
DOI : 10.1016/S0005-1098(01)00278-3

A. Kugi, Nonlinear Control Based on Physical Models, 2001.

R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control, ser. Communications and Control Engineering Series, 2000.

E. Garcia-canseco, D. Jeltsema, J. Scherpen, and R. Ortega, Power???based control of physical systems: two case studies, Proc. 17 th IFAC World Congress, 2008.
DOI : 10.3182/20080706-5-KR-1001.00431

D. Jeltsema and J. M. Scherpen, On mechanical mixed potential, content and co-content, Proc. European Control Conference, pp.73-78, 2003.

R. Ortega, D. Jeltsema, and J. Scherpen, Power shaping: A new paradigm for stabilization of nonlinear RLC circuits, IEEE Transactions on Automatic Control, vol.48, issue.10, pp.1762-1767, 2003.
DOI : 10.1109/TAC.2003.817918

D. Eberard, B. Maschke, A. Van, and . Schaft, Energy-conserving formulation of RLC-circuits with linear resistors, Proc. 17 th International Symposium on Mathematical Theory of Networks and Systems, 2006.

M. Dalsmo, A. Van, and . Schaft, On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems, SIAM Journal on Control and Optimization, vol.37, issue.1, pp.54-91, 1999.
DOI : 10.1137/S0363012996312039

J. Ortega and V. Planas-bielsa, Dynamics on Leibniz manifolds, Journal of Geometry and Physics, vol.52, issue.1, pp.1-27, 2004.
DOI : 10.1016/j.geomphys.2004.01.002
URL : https://hal.archives-ouvertes.fr/hal-00023613

J. Willems, Dissipative dynamical systems part I: General theory, Archive for Rational Mechanics and Analysis, vol.34, issue.No. 4, pp.321-351, 1972.
DOI : 10.1007/BF00276493

J. Gibbs, The Collected Works of J.Willard Gibbs. Longman's, Green and Co, 1931.

C. Carathéodory, Untersuchungen über die Grundlagen der Thermodynamik, Math. Ann, vol.67, 1909.

V. Arnold, Mathematical Methods of Classical Mechanics (translated by K. Vogtmann), 2nd ed., ser. Graduate texts in mathematics, 1989.

R. Mruga?a, Geometrical formulation of equilibrium phenomenological thermodynamics, Reports on Mathematical Physics, vol.14, issue.3, pp.419-427, 1978.
DOI : 10.1016/0034-4877(78)90010-1

R. Mruga?a, J. Nulton, J. Schön, and P. Salamon, Contact structure in thermodynamic theory, Reports on Mathematical Physics, vol.29, issue.1, pp.109-121, 1991.
DOI : 10.1016/0034-4877(91)90017-H

P. Libermann and C. Marle, Symplectic Geometry and Analytical Mechanics, 1987.
DOI : 10.1007/978-94-009-3807-6

D. Eberard, B. Maschke, A. Van, and . Schaft, CONSERVATIVE SYSTEMS WITH PORTS ON CONTACT MANIFOLDS, Proc. 16 th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.00711

D. Eberard, Extension des systèmes hamiltoniens à ports aux systèmes irréversibles: une approche par la géométrie de contact, 2006.

A. Favache, B. Maschke, and D. Dochain, Contact structures: application to interconnected thermodynamical systems, Proc. European Control Conference, 2007.

M. Grmela, Reciprocity relations in thermodynamics Physica A: Statistical Mechanics and its Applications, pp.304-328, 2002.

R. Mruga?a, Submanifolds in the thermodynamic phase space, Reports on Mathematical Physics, vol.21, issue.2, pp.197-203, 1985.
DOI : 10.1016/0034-4877(85)90059-X

C. Godbillon, Géométrie différentielle et mécanique analytique, 1969.

H. Callen, Thermodynamics and an Introduction to Thermostatics, 1985.

S. I. Sandler, Chemical and Engineering Thermodynamics, 1999.

R. Mruga?a, On a special family of thermodynamic processes and their invariants, Reports on Mathematical Physics, vol.46, issue.3, pp.461-468, 2000.
DOI : 10.1016/S0034-4877(00)90012-0

E. Kreyszig, Introductory Functional Analysis with Applications, 1989.

S. De-groot and P. Mazur, Non-Equilibrium Thermodynamics, 1984.

D. Eberard, B. Maschke, A. Van, and . Schaft, On the interconnection structures of open physical systems, Proc