M. Ahmadi, G. Valmorbida, and A. Papachristodoulou, Dissipation inequalities for the analysis of a class of PDEs, Automatica, vol.66, pp.163-171, 2016.

M. Barreau, F. Gouaisbaut, and A. Seuret, Practical stability analysis of a drilling pipe under friction with a PI-controller. IEEE Transaction on Control Systems Technologies, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02099459

M. Barreau, A. Seuret, F. Gouaisbaut, and L. Baudouin, Lyapunov stability analysis of a string equation coupled with an ordinary differential system, IEEE Transactions on Automatic Control, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01548256

L. Baudouin, A. Seuret, and F. Gouaisbaut, Stability analysis of a system coupled to a heat equation, Automatica, vol.99, pp.195-202, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01566455

R. Courant and D. Hilbert, Methods of mathematical physics, 1989.

R. F. Curtain and H. J. Zwart, An introduction to infinite-dimensional linear systems theory, Texts in Applied Mathematics, vol.21, 1995.

E. Fridman, Introduction to Time-Delay Systems, Analysis and Control. Birkhäuser, 2014.

M. Fu, H. Li, and S. I. Niculescu, Robust stability and stabilization of time-delay systems via integral quadratic constraint approach, Stability and control of time-delay systems, 1998.

K. Gu, V. L. Kharitonov, C. , and J. , Stability of time-delay systems, Control engineering. Birkhuser, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00664367

C. P. Gupta, Existence and uniqueness theorems for the bending of an elastic beam equation, Applicable Analysis, vol.26, issue.4, pp.289-304, 1988.

M. Jun and M. G. Safonov, Multiplier IQCs for uncertain time delays, Journal of the Franklin Institute, vol.338, issue.2-3, pp.335-351, 2001.

A. Megretski and A. Rantzer, System analysis via integral quadratic constraints, IEEE Transactions on Automatic Control, vol.42, issue.6, pp.819-830, 1997.

J. W. Miles, The Korteweg-de Vries equation: a historical essay, Journal of fluid mechanics, vol.106, pp.131-147, 1981.

M. Safi, L. Baudouin, and A. Seuret, Tractable sufficient stability conditions for a system coupling linear transport and differential equations, Systems & Control Letters, vol.110, pp.1-8, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01354073

C. W. Scherer and J. Veenman, Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions, Systems Control Letters, vol.121, pp.7-15, 2018.

A. Seuret and F. Gouaisbaut, Hierarchy of LMI conditions for the stability analysis of time delay systems, Systems and Control Letters, vol.81, pp.1-7, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01065142

R. Sipahi, S. I. Niculescu, C. T. Abdallah, W. Michiels, and K. Gu, Stability and stabilization of systems with time delay, IEEE Control Systems, vol.31, issue.1, pp.38-65, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00664367

R. Skelton, T. Iwasaki, and D. Grigoriadis, A Unified Algebraic Approach To Control Design. Series in Systems and Control, 1997.

J. Veenman, C. W. Scherer, and H. Köroglu, Robust stability and performance analysis based on integral quadratic constraints, European Journal of Control, vol.31, pp.1-32, 2016.

J. C. Willems, Dissipative dynamical systems part II: Linear systems with quadratic supply rates. Archive for rational mechanics and analysis, vol.45, pp.352-393, 1972.

J. C. Willems and J. W. Polderman, Introduction to mathematical systems theory: a behavioral approach, vol.26, 2013.