G. Bastin, J. Coron, and B. , Using hyperbolic systems of balance laws for modeling, control and stability analysis of physical networks, Lecture notes for the Pre-Congress Workshop on Complex Embedded and Networked Control Systems 17th IFAC World Congress, 2008.

G. Bastin, J. Coron, and B. , On Lyapunov stability of linearised Saint-Venant equations for a sloping channel, Networks and Heterogeneous Media, pp.177-187, 2009.

T. Cazenave and A. Haraux, An introduction to semilinear evolution equations, 1998.

R. M. Colombo, G. Guerra, M. Herty, and V. Schleper, Optimal Control in Networks of Pipes and Canals, SIAM Journal on Control and Optimization, vol.48, issue.3, pp.2032-2050, 2009.
DOI : 10.1137/080716372

J. 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

J. Coron, G. Bastin, and B. , 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

J. Coron, B. Novel, and G. Bastin, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.2-11, 2007.
DOI : 10.1109/CDC.2004.1428994

J. Coron and E. Trélat, GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS, Communications in Contemporary Mathematics, vol.08, issue.04, pp.535-567, 2006.
DOI : 10.1142/S0219199706002209
URL : https://hal.archives-ouvertes.fr/hal-00086370

S. Dashkovskiy and A. Mironchenko, On the uniform input-to-state stability of reactiondiffusion systems, 49th IEEE Conference on Decision and Control (CDC), pp.6547-6552, 2010.

A. Diagne, G. Bastin, and J. Coron, Lyapunov exponential stability of linear hyperbolic systems of balance laws, Automatica

M. Dick, M. Gugat, and G. Leugering, Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Networks and Heterogeneous Media, pp.691-709, 2010.

V. , D. Santos, and C. Prieur, Boundary control of open channels with numerical and experimental validations, IEEE Transactions on Control Systems Technology, vol.16, issue.6, pp.1252-1264, 2008.

W. H. Graf, Hydraulics of sediment transport, Water Resources Publications, Highlands Ranch, 1984.

W. H. Graf, Fluvial hydraulics, 1998.

M. Gugat, M. Herty, A. Klar, and G. Leugering, Optimal Control for Traffic Flow Networks, Journal of Optimization Theory and Applications, vol.63, issue.3, pp.589-616, 2005.
DOI : 10.1007/s10957-005-5499-z

M. Gugat and G. Leugering, Global boundary controllability of the Saint-Venant system for sloped canals with friction. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, pp.257-270, 2009.

B. Haut and G. Bastin, A second order model of road junctions in fluid models of traffic networks, Networks and Heterogeneous Media, pp.227-253, 2007.
DOI : 10.3934/nhm.2007.2.227

J. Hudson and P. K. Sweby, Formulations for numerically approximating hyperbolic systems governing sediment transport, Journal of Scientific Computing, vol.19, issue.1/3, pp.225-252, 2003.
DOI : 10.1023/A:1025304008907

B. Jayawardhana, H. Logemann, and E. P. Ryan, The Circle Criterion and Input-to-State Stability, IEEE Control Systems, vol.31, issue.4, pp.32-67, 2011.
DOI : 10.1109/MCS.2011.941143

I. Kmit, Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems, International Journal of Dynamical Systems and Differential Equations, vol.1, issue.3, pp.191-195, 2008.
DOI : 10.1504/IJDSDE.2008.019680

M. Krstic and A. Smyshlyaev, Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays, Systems & Control Letters, vol.57, issue.9, pp.750-758, 2008.
DOI : 10.1016/j.sysconle.2008.02.005

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

J. Löfberg, YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), 2004.
DOI : 10.1109/CACSD.2004.1393890

Z. Luo, B. Guo, and O. Morgul, Stability and stabilization of infinite dimensional systems and applications. Communications and Control Engineering, 1999.

P. Malaterre, D. C. 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)

M. Malisoff and F. Mazenc, Constructions of Strict Lyapunov Functions. Communications and Control Engineering Series, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00858552

F. Mazenc, M. Malisoff, and O. Bernard, A Simplified Design for Strict Lyapunov Functions Under Matrosov Conditions, IEEE Transactions on Automatic Control, vol.54, issue.1, pp.177-183, 2009.
DOI : 10.1109/TAC.2008.2008353
URL : https://hal.archives-ouvertes.fr/hal-00858530

F. Mazenc, M. Malisoff, and Z. Lin, Further results on input-to-state stability for nonlinear systems with delayed feedbacks, Automatica, vol.44, issue.9, pp.2415-2421, 2008.
DOI : 10.1016/j.automatica.2008.01.024
URL : https://hal.archives-ouvertes.fr/hal-00857808

F. Mazenc and D. Nesic, Lyapunov functions for time-varying systems satisfying generalized conditions of Matrosov theorem, Mathematics of Control, Signals, and Systems, vol.41, issue.4, pp.151-182, 2007.
DOI : 10.1007/s00498-007-0015-7

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

V. T. Pham, D. Georges, and G. Besancon, Predictive Control with guaranteed stability for hyperbolic systems of conservation laws, 49th IEEE Conference on Decision and Control (CDC), pp.6932-6937, 2010.
DOI : 10.1109/CDC.2010.5718009
URL : https://hal.archives-ouvertes.fr/hal-00551283

C. Prieur and J. De-halleux, Stabilization of a 1-D tank containing a fluid modeled by the shallow water equations, Systems & Control Letters, vol.52, issue.3-4, pp.3-4167, 2004.
DOI : 10.1016/j.sysconle.2003.11.008

C. Prieur, J. Winkin, and G. Bastin, Robust boundary control of systems of conservation laws, Mathematics of Control, Signals, and Systems, vol.124, issue.1, pp.173-197, 2008.
DOI : 10.1007/s00498-008-0028-x

L. F. Shampine, Solving Hyperbolic PDEs in MATLAB, Applied Numerical Analysis & Computational Mathematics, vol.275, issue.3, pp.346-358, 2005.
DOI : 10.1002/anac.200510025

L. F. Shampine, Two-step Lax???Friedrichs method, Applied Mathematics Letters, vol.18, issue.10, pp.1134-1136, 2005.
DOI : 10.1016/j.aml.2004.11.007
URL : http://doi.org/10.1016/j.aml.2004.11.007

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, Input to State Stability: Basic Concepts and Results, Nonlinear and Optimal Control Theory, pp.163-220, 2007.
DOI : 10.1007/978-3-540-77653-6_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.5962

J. F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, pp.11-12625, 1999.
DOI : 10.1080/10556789908805766
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.6954

C. 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