R. Bellman and K. Cooke, Differential-difference equations, 1963.

B. Levin, Distribution of zeros of entire functions, Translations of Mathematical Monographs, 1964.

W. Michiels and S. Niculescu, Stability and stabilization of time-delay systems, of Advances in Design and Control, 2007.
DOI : 10.1137/1.9780898718645

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

W. Govaerts, J. Guckenheimer, and A. Khibnik, Defining Functions for Multiple Hopf Bifurcations, SIAM Journal on Numerical Analysis, vol.34, issue.3, pp.1269-1288, 1997.
DOI : 10.1137/S0036142995282182

M. Dellnitz and B. Werner, Computational methods for bifurcation problems with symmetries???with special attention to steady state and Hopf bifurcation points, Journal of Computational and Applied Mathematics, vol.26, issue.1-2, pp.97-123, 1989.
DOI : 10.1016/0377-0427(89)90150-7

J. Vanbiervliet, K. Verheyden, W. Michiels, and S. Vandewalle, A nonsmooth optimisation approach for the stabilisation of time-delay systems, ESAIM: Control, Optimisation and Calculus of Variations, vol.69, issue.3, pp.478-493, 2008.
DOI : 10.1103/PhysRevE.69.036702

I. Boussaada and S. I. Niculescu, Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach, IEEE Transactions on Automatic Control, vol.61, issue.6, pp.1601-1606, 2016.
DOI : 10.1109/TAC.2015.2480175

URL : https://hal.archives-ouvertes.fr/hal-01425757

I. Boussaada and S. Niculescu, Characterizing the Codimension of Zero Singularities for Time-Delay Systems, Acta Applicandae Mathematicae, vol.4, issue.2, pp.47-88, 2016.
DOI : 10.1007/BFb0088788

URL : https://hal.archives-ouvertes.fr/hal-01429961

I. Boussaada and S. Niculescu, Computing the codimension of the singularity at the origin for delay systems: The missing link with Birkhoff incidence matrices, 21st International Symposium on Mathematical Theory of Networks and Systems, pp.1-8, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01123621

G. Pólya and G. , Szeg? o, Problems and Theorems in Analysis I: Series, Integral Calculus, Theory of Functions, 1972.

A. Ramirez, S. Mondie, R. Garrido, and R. Sipahi, Design of proportional-integral-retarded (pir) controllers for secondorder lti systems, IEEE Transactions on Automatic Control, issue.99, pp.1-6, 2015.

T. Vyhlidal and P. Zitek, Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros, IEEE Transactions on Automatic Control, vol.54, issue.1, pp.171-177, 2009.
DOI : 10.1109/TAC.2008.2008345

I. Boussaada, H. Unal, and S. Niculescu, Multiplicity and stable varieties of time-delay systems: A missing link, Proceeding of the 22nd International Symposium on Mathematical Theory of Networks and Systems, pp.1-6, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01658365

I. Boussaada, S. Niculescu, S. Tliba, and T. Vyhlidal, On the Coalescence of Spectral Values and its Effect on the Stability of Time-delay Systems: Application to Active Vibration Control, IUTAM Symposium on Nonlinear and Delayed Dynamics of Mechatronic Systems, pp.75-82, 2017.
DOI : 10.1016/j.piutam.2017.08.011

URL : https://hal.archives-ouvertes.fr/hal-01656723

K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain Journal of Mathematics, vol.9, issue.1, pp.31-42, 1979.
DOI : 10.1216/RMJ-1979-9-1-31

S. Ruan, DELAY DIFFERENTIAL EQUATIONS IN SINGLE SPECIES DYNAMICS, Fields Inst. Commun, vol.29, pp.477-517, 2006.
DOI : 10.1007/1-4020-3647-7_11

S. Niculescu, W. Michiels, K. Gu, and C. T. Abdallah, Delay Effects on Output Feedback Control of Dynamical Systems, pp.63-84, 2010.
DOI : 10.1007/978-3-642-02329-3_3

O. Kirillov and M. Overton, Robust stability at the Swallowtail singularity, Frontiers in Physics, vol.1, issue.24, 2013.
DOI : 10.3389/fphy.2013.00024

URL : https://hal.archives-ouvertes.fr/hal-00921091

W. Michiels, I. Boussaada, and S. Niculescu, An Explicit Formula for the Splitting of Multiple Eigenvalues for Nonlinear Eigenvalue Problems and Connections with the Linearization for the Delay Eigenvalue Problem, SIAM Journal on Matrix Analysis and Applications, vol.38, issue.2, pp.599-620, 2017.
DOI : 10.1137/16M107774X

URL : https://hal.archives-ouvertes.fr/hal-01558169

S. Tliba, Control of a Vibrating Axisymmetric Membrane using Piezoelectric Transducers, 18th IFAC World Congress, p.7713, 2011.
DOI : 10.3182/20110828-6-IT-1002.03518

URL : https://hal.archives-ouvertes.fr/hal-00625579

E. Park and J. Mills, Static Shape and Vibration Control of Flexible Payloads With Applications to Robotic Assembly, IEEE/ASME Transactions on Mechatronics, vol.10, issue.6, pp.675-687, 2005.
DOI : 10.1109/TMECH.2005.859836

W. Juan, H. Hongsheng, Q. Suxiang, and Q. Linfang, Research on Shape Control and Active Vibration Control of Piezoelectric Composite Laminated Shell, 2007 8th International Conference on Electronic Measurement and Instruments, pp.4-569, 2007.
DOI : 10.1109/ICEMI.2007.4351208

W. Chen, M. Buehler, G. Parker, and B. Bettig, Optimal Sensor Design and Control of Piezoelectric Laminate Beams, IEEE Transactions on Control Systems Technology, vol.12, issue.1, pp.148-155, 2004.
DOI : 10.1109/TCST.2003.822483

H. Banks, R. Del-rosario, and H. Tran, Proper orthogonal decomposition-based control of transverse beam vibrations: experimental implementation, IEEE Transactions on Control Systems Technology, vol.10, issue.5, pp.717-726, 2002.
DOI : 10.1109/TCST.2002.801793

M. Kögl and M. L. Bucalem, Analysis of smart laminates using piezoelectric MITC plate and shell elements, Computers & Structures, vol.83, issue.15-16, pp.1153-1163, 2005.
DOI : 10.1016/j.compstruc.2004.08.024

DOI : 10.3182/20050703-6-CZ-1902.00527

URL : https://hal.archives-ouvertes.fr/hal-00527358

S. Tliba, Contrôle actif des vibrations dans des structures mécaniques minces instrumentées de transducteurs piézoélectriques, Thèse de doctorat, 2004.

M. Gérardin and D. Rixen, Mechanical vibrations: theory and application to structural dynamics, 1997.

L. Komzsik, What every engineer should know about computational techniques of finite element analysis, 2005.
DOI : 10.1201/b15951

A. Benjeddou, Advances in piezoelectric finite element modeling of adaptive structural elements: a survey, Computers & Structures, vol.76, issue.1-3, pp.347-363, 2000.
DOI : 10.1016/S0045-7949(99)00151-0

A. Preumont, Vibration Control of Active Structure, An Introduction, 2nd Edition, Solid Mechanics and its Applications, 2002.