M. Barreau, F. Gouaisbaut, A. Seuret, and R. Sipahi, Input / output stability of a damped string equation coupled with ordinary differential system, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01690626

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

G. Bastin and J. Coron, Stability and boundary stabilization of 1-d hyperbolic systems, vol.88, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01449504

L. Baudouin, A. Seuret, and F. Gouaisbaut, Lyapunov stability analysis of a linear system coupled to a heat equation, 20th IFAC World Congress, vol.50, pp.11978-11983, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01496115

L. Baudouin, A. Seuret, and M. Safi, Stability analysis of a system coupled to a transport equation using integral inequalities, 2nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations (CPDE), vol.49, pp.92-97, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01310306

D. Bresch-pietri and M. Krstic, Output-feedback adaptive control of a wave PDE with boundary anti-damping, Automatica, 2014.

N. Challamel, Rock destruction effect on the stability of a drilling structure, Journal of sound and vibration, vol.233, issue.2, pp.235-254, 2000.

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

R. Datko, Two questions concerning the boundary control of certain elastic systems, Journal of Differential Equations, vol.92, issue.1, pp.27-44, 1991.

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

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.

J. K. Hale and S. M. Lunel, Effects of small delays on stability and control, Operator theory and analysis, pp.275-301, 2001.
DOI : 10.1007/978-3-0348-8283-5_10

W. He, S. Zhang, and S. S. Ge, Adaptive control of a flexible crane system with the boundary output constraint, IEEE Transactions on Industrial Electronics, vol.61, issue.8, pp.4126-4133, 2014.

M. Krstic, Delay compensation for nonlinear, adaptive, and PDE systems, 2009.
DOI : 10.1007/978-0-8176-4877-0

M. Krstic and A. Smyshlyaev, Boundary control of PDEs: A course on backstepping designs, vol.16, 2008.

¨. O. Morgül, A dynamic control law for the wave equation, Automatica, vol.30, issue.11, pp.1785-1792, 1994.

N. Olgac and R. Sipahi, A practical method for analyzing the stability of neutral type LTI-time delayed systems, Automatica, vol.40, issue.5, pp.847-853, 2004.

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.
DOI : 10.1016/j.sysconle.2017.09.003
URL : https://hal.archives-ouvertes.fr/hal-01354073

B. Saldivar, H. Boussaada, S. Mounier, and . Niculescu, Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01123773

B. Saldivar, S. Mondié, and J. C. Avila-vilchis, The control of drilling vibrations: A coupled PDE-ODE modeling approach, International Journal of Applied Mathematics and Computer Science, 2016.

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

A. Terrand-jeanne, V. Martins, and V. Andrieu, Regulation of the downside angular velocity of a drilling string with a P-I controller, pp.2647-2652, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02014813

M. Tucsnak and G. Weiss, Observation and control for operator semigroups, 2009.
DOI : 10.1007/978-3-7643-8994-9
URL : https://hal.archives-ouvertes.fr/hal-00590673

H. Wu and J. Wang, Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE-beam systems, Automatica, vol.50, issue.11, pp.2787-2798, 2014.
DOI : 10.1016/j.automatica.2014.09.006