F. Alabau-boussouira, V. Perrollaz, and L. Rosier, Finite-time stabilization of a network of strings, Mathematical Control and Related Fields, vol.5, issue.4, pp.721-742, 2015.
DOI : 10.3934/mcrf.2015.5.721
URL : https://hal.archives-ouvertes.fr/hal-01261807

S. Amin, F. M. Hante, and A. M. Bayen, Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems, IEEE Transactions on Automatic Control, vol.57, issue.2, pp.291-301, 2012.
DOI : 10.1109/TAC.2011.2158171

C. E. Avellar and J. K. Hale, On the zeros of exponential polynomials, Journal of Mathematical Analysis and Applications, vol.73, issue.2, pp.73-434, 1980.
DOI : 10.1016/0022-247X(80)90289-9

G. Bastin, B. Haut, J. Coron, and B. D. , Andréa-Novel, Lyapunov stability analysis of networks of scalar conservation laws, Netw. Heterog. Media, issue.2, pp.751-759, 2007.

R. K. Brayton, Bifurcation of periodic solutions in a nonlinear difference-differential equations of neutral type, Quarterly of Applied Mathematics, vol.24, issue.3, pp.215-224, 1966.
DOI : 10.1090/qam/204800

A. Bressan, S. Cani´ccani´c, M. Garavello, M. Herty, and B. Piccoli, Flows on networks: recent results and perspectives, EMS Surveys in Mathematical Sciences, vol.1, issue.1, pp.47-111, 2014.
DOI : 10.4171/EMSS/2

Y. Chitour, G. Mazanti, and M. Sigalotti, Persistently damped transport equation on a network of circles, Trans. Amer. Math. Soc

K. L. Cooke and D. W. Krumme, Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations, Journal of Mathematical Analysis and Applications, vol.24, issue.2, pp.372-387, 1968.
DOI : 10.1016/0022-247X(68)90038-3

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

R. Dáger and E. Zuazua, Wave propagation, observation and control in 1-d flexible multistructures, of Mathématiques & Applications, 2006.

E. Fridman, S. Mondié, and B. Saldivar, Bounds on the response of a drilling pipe model, IMA Journal of Mathematical Control and Information, vol.27, issue.4, pp.513-526, 2010.
DOI : 10.1093/imamci/dnq024

J. J. Green, Uniform Convergence to the Spectral Radius and Some Related Properties in Banach Algebras, 1996.

M. Gugat, M. Herty, A. Klar, G. Leugering, and V. Schleper, Well-posedness of Networked Hyperbolic Systems of Balance Laws, Constrained optimization and optimal control for partial differential equations, pp.123-146, 2012.
DOI : 10.1007/978-3-0348-0133-1_7

M. Gugat and M. Sigalotti, Stars of vibrating strings: switching boundary feedback stabilization, Netw. Heterog. Media, vol.5, pp.299-314, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00589697

J. K. Hale and S. M. , Introduction to functional differential equations, of Applied Mathematical Sciences, 1993.
DOI : 10.1007/978-1-4612-4342-7

F. M. Hante, G. Leugering, and T. I. Seidman, Modeling and Analysis of Modal Switching in??Networked Transport Systems, Applied Mathematics and Optimization, vol.3, issue.4
DOI : 10.1007/s00245-008-9057-6

R. Jungers, The joint spectral radius, Theory and applications Lecture Notes in Control and Information Sciences, vol.385, 2009.
DOI : 10.1007/978-3-540-95980-9

B. Klöss, The flow approach for waves in networks, Operators and Matrices, vol.6, issue.1, pp.107-128, 2012.
DOI : 10.7153/oam-06-08

D. Liberzon, Switching in Systems and Control, 2003.
DOI : 10.1007/978-1-4612-0017-8

W. Michiels, T. Vyhlídal, P. Zítek, H. Nijmeijer, and D. Henrion, Strong Stability of Neutral Equations with an Arbitrary Delay Dependency Structure, SIAM Journal on Control and Optimization, vol.48, issue.2, pp.48-763, 2009.
DOI : 10.1137/080724940

W. L. Miranker, Periodic Solutions of the Wave Equation with a Nonlinear Interface Condition, IBM Journal of Research and Development, vol.5, issue.1, pp.2-24, 1961.
DOI : 10.1147/rd.51.0002

P. H. Ngoc and N. D. Huy, Exponential stability of linear delay difference equations with continuous time, Vietnam Journal of Mathematics, vol.42, pp.1-11, 2014.

C. Prieur, A. Girard, and E. Witrant, Stability of Switched Linear Hyperbolic Systems by Lyapunov Techniques, IEEE Transactions on Automatic Control, vol.59, issue.8, pp.59-2196, 2014.
DOI : 10.1109/TAC.2013.2297191
URL : https://hal.archives-ouvertes.fr/hal-00845766

W. Rudin, Real and complex analysis, 1987.

E. J. Schmidt, On the Modelling and Exact Controllability of Networks of Vibrating Strings, SIAM Journal on Control and Optimization, vol.30, issue.1, pp.229-245, 1992.
DOI : 10.1137/0330015

M. Slemrod, Nonexistence of oscillations in a nonlinear distributed network, Journal of Mathematical Analysis and Applications, vol.36, issue.1, pp.22-40, 1971.
DOI : 10.1016/0022-247X(71)90016-3

Z. Sun and S. S. Ge, Stability theory of switched dynamical systems, Communications and Control Engineering Series, 2011.
DOI : 10.1007/978-0-85729-256-8

J. Valein and E. Zuazua, Stabilization of the Wave Equation on 1-d Networks, SIAM Journal on Control and Optimization, vol.48, issue.4, pp.2771-2797, 2009.
DOI : 10.1137/080733590

E. Zuazua, Control and stabilization of waves on 1-d networks, in Modelling and Optimisation of Flows on Networks, pp.463-493, 2013.