Z. Artstein, Linear systems with delayed controls: A reduction, IEEE Transactions on Automatic Control, vol.27, issue.4, pp.869-879, 1982.
DOI : 10.1109/TAC.1982.1103023

N. Bekiaris-liberis and M. Krstic, Nonlinear Control under Nonconstant Delays, Society for Industrial and Applied Mathematics
DOI : 10.1137/1.9781611972856

N. Bekiaris-liberis and M. Krstic, Nonlinear control under delays that depend on delayed states, European Journal of Control, vol.19, issue.5, pp.389-398, 2013.
DOI : 10.1016/j.ejcon.2013.05.016

N. Bekiaris-liberis and M. Krstic, Compensation of State-Dependent Input Delay for Nonlinear Systems, IEEE Transactions on Automatic Control, vol.58, issue.2, pp.275-289, 2013.
DOI : 10.1109/TAC.2012.2208294

N. Bekiaris-liberis and M. Krstic, Robustness of nonlinear predictor feedback laws to time- and state-dependent delay perturbations, Automatica, vol.49, issue.6, pp.1576-1590, 2013.
DOI : 10.1016/j.automatica.2013.02.050

M. B. Saldivar-marquez, I. Boussaada, H. Mounier, and S. Niculescu, Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach, 2015.
DOI : 10.1007/978-3-319-15747-4

D. Bresch-pietri, J. Chauvin, and N. Petit, Adaptive control scheme for uncertain time-delay systems, Automatica, vol.48, issue.8, pp.1536-1552, 2012.
DOI : 10.1016/j.automatica.2012.05.056

URL : https://hal.archives-ouvertes.fr/hal-00733308

D. Bresch-pietri, J. Chauvin, and N. Petit, Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type, IEEE Transactions on Automatic Control, vol.59, issue.9, pp.2385-2399, 2014.
DOI : 10.1109/TAC.2014.2322238

URL : https://hal.archives-ouvertes.fr/hal-01059870

D. Bresch-pietri and N. Petit, Robust compensation of a chattering time-varying input delay, 53rd IEEE Conference on Decision and Control, pp.457-462, 2014.
DOI : 10.1109/CDC.2014.7039423

URL : https://hal.archives-ouvertes.fr/hal-01100071

J. Dieulot and J. Richard, Tracking control of a nonlinear system with input-dependent delay, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), pp.4027-4031, 2001.
DOI : 10.1109/CDC.2001.980523

R. Downey, R. Kamalapurkar, N. Fischer, and W. Dixon, Compensating for Fatigue-Induced Time-Varying Delayed Muscle Response in Neuromuscular Electrical Stimulation Control, Recent Results on Nonlinear Time Delayed Systems, pp.143-161, 2015.
DOI : 10.1007/978-3-319-18072-4_7

L. Figueredo, J. Ishihara, G. Borges, and A. Bauchspiess, Robust stability criteria for uncertain systems with delay and its derivative varying within intervals, Proceedings of the American Control Conference, pp.4884-4889, 2011.

E. Fridman and S. Niculescu, On complete Lyapunov???Krasovskii functional techniques for uncertain systems with fast-varying delays, International Journal of Robust and Nonlinear Control, vol.40, issue.3, pp.364-374, 2008.
DOI : 10.1007/978-1-4612-0039-0

E. Fridman, A. Seuret, and J. Richard, Robust sampled-data stabilization of linear systems: an input delay approach, Automatica, vol.40, issue.8, pp.1441-1446, 2004.
DOI : 10.1016/j.automatica.2004.03.003

URL : https://hal.archives-ouvertes.fr/inria-00131031

E. Fridman and U. Shaked, Delay-dependent stability and H ??? control: Constant and time-varying delays, International Journal of Control, vol.269, issue.1, pp.48-60, 2003.
DOI : 10.1080/00207170210123833

H. Gao, T. Chen, and J. Lam, A new delay system approach to network-based control, Automatica, vol.44, issue.1, pp.39-52, 2008.
DOI : 10.1016/j.automatica.2007.04.020

K. Gu, V. Kharitonov, and J. Chen, Stability of Time-Delay Systems, 2003.
DOI : 10.1007/978-1-4612-0039-0

URL : https://hal.archives-ouvertes.fr/hal-00664367

I. Haidar, P. Mason, S. Niculescu, M. Sigalotti, and A. Chaillet, Further remarks on Markus-Yamabe instability for time-varying delay differential equations, Proceedings of the 12th IFAC Workshop on Time Delay Systems, pp.33-38, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01632829

A. Halanay, Differential Equations: Stability, Oscillations, Time Lags, 1966.

J. Hale, Ordinary Differential Equations, 1980.

A. Ivanov, E. Liz, and S. Trofimchuk, Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima, Tohoku Mathematical Journal, vol.54, issue.2, pp.277-295, 2002.
DOI : 10.2748/tmj/1113247567

M. Jankovic, Recursive predictor design for linear systems with time delay, 2008 American Control Conference, pp.4904-4909, 2008.
DOI : 10.1109/ACC.2008.4587271

I. Karafyllis and M. Krstic, On the relation of delay equations to first-order hyperbolic partial differential equations, ESAIM: Control, Optimisation and Calculus of Variations, vol.20, issue.3, pp.894-923, 2014.
DOI : 10.1051/cocv:2002062

I. Karafyllis, M. Malisoff, and M. Krstic, Sampled-data feedback stabilization of age-structured chemostat models, 2015 American Control Conference (ACC), pp.4549-4554
DOI : 10.1109/ACC.2015.7172045

H. Khalil, Nonlinear Systems, Third Edition, 2002.

V. Kharitonov and S. Niculescu, On the stability of linear systems with uncertain delay, IEEE Transactions on Automatic Control, vol.48, issue.1, pp.127-132, 2002.
DOI : 10.1109/TAC.2002.806665

M. Krstic, Delay Compensation for Nonlinear, Adaptive, and PDE Systems, 2009.
DOI : 10.1007/978-0-8176-4877-0

M. Krstic, Lyapunov Stability of Linear Predictor Feedback for Time-Varying Input Delay, IEEE Transactions on Automatic Control, vol.55, issue.2, pp.554-559, 2010.
DOI : 10.1109/TAC.2009.2038196

W. Kwon and A. Pearson, Feedback stabilization of linear systems with delayed control, IEEE Transactions on Automatic Control, vol.25, issue.2, pp.266-269, 1980.
DOI : 10.1109/TAC.1980.1102288

K. Liu, V. Suplin, and E. Fridman, Stability of linear systems with general sawtooth delay, IMA Journal of Mathematical Control and Information, vol.27, issue.4, pp.419-436, 2010.
DOI : 10.1093/imamci/dnq023

A. Manitius and A. Olbrot, Finite spectrum assignment problem for systems with delays, IEEE Transactions on Automatic Control, vol.24, issue.4, pp.541-552, 1979.
DOI : 10.1109/TAC.1979.1102124

L. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Mathematical Journal, vol.12, issue.2, pp.305-317, 1960.

F. Mazenc and M. Malisoff, New technique for stability analysis for time-varying systems with delay, 53rd IEEE Conference on Decision and Control, pp.1215-1220, 2014.
DOI : 10.1109/CDC.2014.7039547

URL : https://hal.archives-ouvertes.fr/hal-01088244

F. Mazenc and M. Malisoff, Trajectory Based Approach for the Stability Analysis of Nonlinear Systems with Time Delays, IEEE Transactions on Automatic Control, vol.60, issue.6, pp.1716-1721, 2015.
DOI : 10.1109/TAC.2014.2361593

URL : https://hal.archives-ouvertes.fr/hal-01100347

F. Mazenc and M. Malisoff, Reduction model approach for systems with a time-varying delay, 2015 54th IEEE Conference on Decision and Control (CDC), pp.7723-7727, 2015.
DOI : 10.1109/CDC.2015.7403440

URL : https://hal.archives-ouvertes.fr/hal-01248071

F. Mazenc, M. Malisoff, and T. Dinh, Robustness of nonlinear systems with respect to delay and sampling of the controls, Automatica, vol.49, issue.6, pp.1925-1931, 2013.
DOI : 10.1016/j.automatica.2013.02.064

URL : https://hal.archives-ouvertes.fr/hal-00823918

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, M. Malisoff, and S. Niculescu, Reduction Model Approach for Linear Time-Varying Systems With Delays, IEEE Transactions on Automatic Control, vol.59, issue.8, pp.2068-2082, 2014.
DOI : 10.1109/TAC.2014.2320308

URL : https://hal.archives-ouvertes.fr/hal-01062761

F. Mazenc, M. Malisoff, and S. Niculescu, Stability analysis for systems with time-varying delay: Trajectory based approach, 2015 54th IEEE Conference on Decision and Control (CDC), pp.1811-1816, 2015.
DOI : 10.1109/CDC.2015.7402473

URL : https://hal.archives-ouvertes.fr/hal-01248070

F. Mazenc, S. Niculescu, and M. Krstic, Lyapunov???Krasovskii functionals and application to input delay compensation for linear time-invariant systems, Automatica, vol.48, issue.7, pp.1317-1323, 2012.
DOI : 10.1016/j.automatica.2012.04.002

URL : https://hal.archives-ouvertes.fr/hal-00761591

W. Michiels and S. Niculescu, Stability and Stabilization of Time-Delay Systems, Society for Industrial and Applied Mathematics, 2007.
DOI : 10.1137/1.9780898718645

URL : https://hal.archives-ouvertes.fr/hal-00664367

S. Mondié and W. Michiels, Finite spectrum assignment of unstable time-delay systems with a safe implementation, IEEE Transactions on Automatic Control, vol.48, issue.12, pp.2207-2212, 2003.
DOI : 10.1109/TAC.2003.820147

N. Petit, Y. Creff, and P. Rouchon, Motion planning for two classes of nonlinear systems with delays depending on the control, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), pp.1007-1011, 1998.
DOI : 10.1109/CDC.1998.760828

J. Richard, Time-delay systems: an overview of some recent advances and open problems, Automatica, vol.39, issue.10, pp.1667-1694, 2003.
DOI : 10.1016/S0005-1098(03)00167-5

W. Rudin, Principles of Mathematical Analysis, Third Edition, 1976.

M. Sbarciog, R. De-keyser, S. Cristea, and C. Prada, Nonlinear Predictive Control of processes with variable time delay. A temperature control case study, 2008 IEEE International Conference on Control Applications, pp.1001-1006, 2008.
DOI : 10.1109/CCA.2008.4629668

O. Smith, A controller to overcome dead time, ISA Journal, vol.6, issue.2, pp.28-33, 1959.

B. Zhou, Truncated Predictor Feedback for Time-Delay Systems, 2014.
DOI : 10.1007/978-3-642-54206-0