E. N. Gryazina, B. T. Polyak, and A. A. Tremba, D-decomposition technique state-of-the-art, Automation and Remote Control, vol.69, issue.12, pp.1991-2026, 2008.
DOI : 10.1134/S0005117908120011

N. G. Chebotarev and N. N. Meiman, The Routh-Hurwitz problem for polynomials and for entire functions, Trudy Matem. Inst. Steklov, vol.26, pp.1-332, 1949.

L. E. El-'sgol-'ts and S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments, 1973.

M. S. Lee and C. S. Hsu, On the $\tau $-Decomposition Method of Stability Analysis for Retarded Dynamical Systems, SIAM Journal on Control, vol.7, issue.2, pp.249-259, 1969.
DOI : 10.1137/0307017

W. Michiels and S. Niculescu, Stability and stabilization of timedelay systems. An eigenvalue based approach, SIAM: Philadelphia, USA, Advances in design and control, 2014.

E. Jarlebring and W. Michiels, Invariance properties in the root sensitivity of time-delay systems with double imaginary roots, Automatica, vol.46, issue.6, pp.1112-1115, 2010.
DOI : 10.1016/j.automatica.2010.03.014

X. Li, S. Niculescu, A. Ela, H. Wang, and T. Cai, On Computing Puiseux Series for Multiple Imaginary Characteristic Roots of LTI Systems With Commensurate Delays, IEEE Transactions on Automatic Control, vol.58, issue.5, pp.1338-1343, 2013.
DOI : 10.1109/TAC.2012.2226102
URL : https://hal.archives-ouvertes.fr/hal-00935428

K. Gu, S. Niculescu, and J. Chen, On stability crossing curves for general systems with two delays, Journal of Mathematical Analysis and Applications, vol.311, issue.1, pp.231-253, 2005.
DOI : 10.1016/j.jmaa.2005.02.034

K. Gu, D. Irofti, I. Boussaada, and S. Niculescu, Migration of double imaginary characteristic roots under small deviation of two delay parameters, 2015 54th IEEE Conference on Decision and Control (CDC), pp.6410-6415, 2015.
DOI : 10.1109/CDC.2015.7403229
URL : https://hal.archives-ouvertes.fr/hal-01261215

J. Sieber and B. Krauskopf, Bifurcation analysis of an inverted pendulum with delayed feedback control near a triple-zero eigenvalue singularity, Nonlinearity, vol.17, issue.1, pp.85-103, 2004.
DOI : 10.1088/0951-7715/17/1/006

I. Boussaada, I. Morarescu, and S. Niculescu, Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains, Systems & Control Letters, vol.82, pp.1-9, 2015.
DOI : 10.1016/j.sysconle.2015.03.002
URL : https://hal.archives-ouvertes.fr/hal-01162266

T. Kato, Perturbation Theory for Linear Operators, 1980.
DOI : 10.1007/978-3-662-12678-3

K. Knopp, Theory of Functions, Parts I and II, Translated to English by F, Bagemihl, 1996.

J. Chen, P. Fu, S. I. Niculescu, and Z. Guan, An Eigenvalue Perturbation Approach to Stability Analysis, Part I: Eigenvalue Series of Matrix Operators, SIAM Journal on Control and Optimization, vol.48, issue.8, pp.48-5564, 2010.
DOI : 10.1137/080741707

J. Chen, P. Fu, S. I. Niculescu, and Z. Guan, An Eigenvalue Perturbation Approach to Stability Analysis, Part II: When Will Zeros of Time-Delay Systems Cross Imaginary Axis?, SIAM Journal on Control and Optimization, vol.48, issue.8, pp.48-5583, 2010.
DOI : 10.1137/080741719

V. L. Kharitonov, S. I. Niculescu, J. A. Pérez, and W. Michiels, Static output feedback stabilization: necessary conditions for multiple delay controllers, IEEE Transactions on Automatic Control, vol.50, issue.1, pp.82-86, 2005.
DOI : 10.1109/TAC.2004.841137