N. Aghannan and P. Rouchon, An intrinsic observer for a class of lagrangian systems, IEEE Transactions on Automatic Control, vol.48, issue.6, pp.936-945, 2003.
DOI : 10.1109/TAC.2003.812778

M. A. Aizerman and F. R. Gantmacher, Absolute Stability of Regulator Systems, 1964.

D. Angeli, A Lyapunov approach to incremental stability properties, IEEE Transactions on Automatic Control, vol.47, issue.3, pp.410-421, 2002.
DOI : 10.1109/9.989067

S. J. Chung and J. J. Slotine, Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems, IEEE Transactions on Robotics, vol.25, issue.3, pp.686-700, 2009.
DOI : 10.1109/TRO.2009.2014125

S. J. Chung and J. J. Slotine, On synchronization of coupled Hopf-Kuramoto oscillators with phase delays, 49th IEEE Conference on Decision and Control (CDC), pp.3181-3187, 2010.
DOI : 10.1109/CDC.2010.5717962

B. Demidovich, Lectures on Stability Theory, 1967.

C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, 1975.
DOI : 10.1137/1.9780898719055

F. Forni and R. Sepulchre, A Differential Lyapunov Framework for Contraction Analysis, IEEE Transactions on Automatic Control, vol.59, issue.3, 2013.
DOI : 10.1109/TAC.2013.2285771

F. R. Gantmacher, The theory of matrices, vols. I and II, 1959.

H. Haidar, W. Pasillas-lépine, E. Panteley, and A. Chaillet, Basal ganglia oscillations: the role of delays and external excitatory nuclei, To appear in Proc. European Control Conference, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00742100

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

C. Hammond, H. Bergman, and P. Brown, Pathological synchronization in Parkinson's disease: networks, models and treatments, INMED/TINS special issue?Physiogenic and pathogenic oscillations: the beauty and the beast, pp.357-364, 2007.
DOI : 10.1016/j.tins.2007.05.004
URL : http://www.hal.inserm.fr/inserm-00483864/file/HammondTINS2007.pdf

Q. Han, Absolute stability of time-delay systems with sector-bounded nonlinearity, Automatica, vol.41, issue.12, pp.412171-2176, 2005.
DOI : 10.1016/j.automatica.2005.08.005

A. J. Nevado-holgado, J. R. Terry, and R. Bogacz, Conditions for the Generation of Beta Oscillations in the Subthalamic Nucleus-Globus Pallidus Network, Journal of Neuroscience, vol.30, issue.37, p.12340, 2010.
DOI : 10.1523/JNEUROSCI.0817-10.2010

B. Jayawardhana, H. Logemann, and E. Ryan, The Circle Criterion and Input-to-State Stability, IEEE Control Systems, vol.31, issue.4, pp.32-67, 2011.
DOI : 10.1109/MCS.2011.941143

H. Khalil, Nonlinear systems, 1996.

W. Lohmiller and J. J. Slotine, On contraction analysis for nonlinear systems, Automatica, vol.34, issue.6, 1998.

W. Michiels and S. Niculescu, Stability and Stabilization of Time- Delay Systems: An Eigenvalue-Based Approach, Advances in Design and Control), 2008.
DOI : 10.1137/1.9780898718645

W. Pasillas-lépine, Delay-induced oscillations in Wilson and Cowan???s model: an analysis of the subthalamo-pallidal feedback loop in healthy and parkinsonian subjects, Biological Cybernetics, vol.12, issue.1, 2013.
DOI : 10.1007/s00422-013-0549-3

A. V. Pavlov, N. Van-de-wouw, and H. Nijmeijer, Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach, Systems & Control: Foundations & Applications, 2006.
DOI : 10.1007/0-8176-4465-2

A. V. Pavlov, N. Van-de-wouw, and H. Nijmeijer, Frequency Response Functions for Nonlinear Convergent Systems, IEEE Transactions on Automatic Control, vol.52, issue.6, pp.1159-1165, 2007.
DOI : 10.1109/TAC.2007.899020
URL : http://repository.tue.nl/647586

V. Pliss, Nonlocal Problems of the Theory of Oscillations, 1966.

G. Pola, P. Pepe, M. D. Benedetto, and P. Tabuada, Symbolic models for nonlinear time-delay systems using approximate bisimulations, Systems & Control Letters, vol.59, issue.6, pp.365-373, 2010.
DOI : 10.1016/j.sysconle.2010.04.001
URL : http://arxiv.org/abs/0903.0361

V. Rasvan, D. Danciu, and D. Popescu, Frequency domain stability inequalities for nonlinear time delay systems, Melecon 2010, 2010 15th IEEE Mediterranean Electrotechnical Conference, pp.1398-1401, 2010.
DOI : 10.1109/MELCON.2010.5476017

B. S. Razumikhin, Application of Liapunov's method to problems in the stability of systems with a delay, Avtomat. i Telemeh, vol.21, pp.740-774, 1960.

G. Russo, M. Di-bernardo, and E. D. Sontag, Global entrainment of transciptional systems to periodic inputs, PLoS Computational Biology, vol.6, issue.4, pp.1-26, 2010.

E. Steur and H. Nijmeijer, Synchronization in Networks of Diffusively Time-Delay Coupled (Semi-)Passive Systems, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.58, issue.6, pp.1358-1371, 2011.
DOI : 10.1109/TCSI.2010.2097670

A. R. Teel, Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem, IEEE Transactions on Automatic Control, vol.43, issue.7, pp.960-964, 1998.
DOI : 10.1109/9.701099

S. Tiwari, Y. Wang, and Z. P. Jiang, Remarks on integral-ISS for systems with delays, Proceedings of the 10th World Congress on Intelligent Control and Automation, p.2012
DOI : 10.1109/WCICA.2012.6358245

V. A. Yakubovich, The matrix-inequality method in the theory of the stability of nonlinear control systems. I: The absolute stability of forced vibrations, Autom. Rem. Control, vol.25, pp.905-917, 1965.