J. M. Ball and M. Slemrod, Feedback stabilization of distributed semilinear control systems, Applied Mathematics and Optimization, vol.5, issue.1, pp.169-179, 1979.

C. Bardos, A. Y. Leroux, and J. C. Nedelec, First order quasilinear equations with boundary conditions, Communications in Partial Differential Equations, vol.4, issue.9, pp.1017-1034, 1979.

G. Bastin and J. Coron, Stability And Boundary Stabilization Of 1-D Hyperbolic Systems. Progress in Nonlinear Differential Equations and Their Applications, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01449504

G. Bastin and J. M. Coron, Dissipative boundary conditions for one-dimensional quasilinear hyperbolic systems: Lyapunov stability for the C 1 norm, SIAM J. Control Optim, vol.53, pp.1464-1483, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01449620

S. Blandin, X. Litrico, M. L. Delle-monache, B. Piccoli, and A. Bayen, Regularity and Lyapunov stabilization of weak entropy solutions to scalar conservation laws, IEEE Transactions on Automatic Control, vol.62, issue.4, pp.1620-1635, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01267722

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2010.

P. J. Campo and M. Morari, Robust control of processes subject to saturation nonlinearities, Computers Chemical Engineering, vol.14, issue.4, pp.343-358, 1990.

J. 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, pp.2-11, 2004.

J. Coron and Z. Wang, Output feedback stabilization for a scalar conservation law with a nonlocal velocity, SIAM Journal on Mathematical Analysis, vol.45, p.2013

N. Espitia, A. Tanwani, and S. Tarbouriech, Stabilization of boundary controlled hyperbolic PDEs via Lyapunov-based event triggered sampling and quantization, Proceedings of the 56th IEEE Conference on Decision and Control, pp.1266-1271, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01856311

A. Hayat, Exponential stability of general 1-D quasilinear systems with source terms for the C 1 norm under boundary conditions, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01613139

M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs, Advances in Design and Control. Society for Industrial and Applied Mathematics, 2008.

I. Lasiecka and T. Seidman, Strong stability of elastic control systems with dissipative saturating feedback, Systems & Control Letters, vol.48, pp.243-252, 2003.

T. T. Li, R. Bopeng, and J. Yi, Semi-global C 1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems, ESAIM: M2AN, vol.34, issue.2, pp.399-408, 2000.

I. Miyadera, Nonlinear Semigroups. Translations of mathematical monographs, 1992.

C. Prieur and F. Ferrante, Boundary control design for linear conservation laws in the presence of energy-bounded measurement noise, Proceedings of the 57th IEEE Conference on Decision and Control, pp.6550-6555, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01880804

C. Prieur, S. Tarbouriech, and J. M. Gomes-da-silva, Wave equation with cone-bounded control laws, IEEE Transactions on Automatic Control, vol.61, issue.11, pp.3452-3463, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01448483

M. Slemrod, Feedback stabilization of a linear control system in Hilbert space with an a priori bounded control, Mathematics of Control, Signals and Systems, vol.2, issue.3, pp.265-285, 1989.

S. Tarbouriech, G. Garcia, J. M. Gomes-da-silva, and I. Queinnec, Stability and Stabilization of Linear Systems with Saturating Actuators, 2011.

C. , Existence of solutions to first-order periodic boundary value problems, Journal of Mathematical Analysis and Applications, vol.323, issue.2, pp.1325-1332, 2006.