A. Bensoussan, G. Da-prato, M. C. Defour, and S. K. Mitter, Representation and control of infinite dimensional systems, Systems & Control: Foundation & Applications, 2 volumes, 1993.

E. W. Kamen, An operator theory of linear functional differential equations, Journal of Differential Equations, vol.27, issue.2, pp.274-297, 1978.

K. L. Cooke and P. Van-den-driessche, On zeroes of some transcendental equations, Funkcialaj Ekvacioj, vol.29, pp.77-90, 1986.

F. G. Boese, Stability with Respect to the Delay: On a Paper of K. L. Cooke and P. van den Driessche, Journal of Mathematical Analysis and Applications, vol.228, issue.2, pp.293-321, 1998.

K. Walton and J. E. Marshall, Direct method for TDS stability analysis, IEE Proceedings D Control Theory and Applications, vol.134, issue.2, pp.101-107, 1987.

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

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.

J. Hale, Theory of Functional Differential Equations, 1977.

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

W. Michiels and &. S. Niculescu, Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach, 2014.

R. Sipahi, S. I. Niculescu, C. T. Abdallah, W. Michiels, K. Gu et al., Stability and Stabilization of Systems with Time DelayHigh-order analysis of critical stability properties of linear time-delay systems, IEEE Control Systems American Control Conference ACC'07, pp.38-65, 2007.

J. Chen, G. Gu, and C. N. Nett, A new method for computing delay margins for stability of linear delay systems, Systems & Control Letters, vol.26, issue.2, pp.107-117, 1995.

E. Beretta and Y. Kuang, Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters, SIAM Journal on Mathematical Analysis, vol.33, issue.5, pp.1144-1165, 2002.

S. A. Gourley and Y. Kuang, A stage structured predator-prey model and its dependence on maturation delay and death rate, Journal of Mathematical Biology, vol.49, issue.2, pp.188-200, 2004.

R. M. Nisbet, W. S. Gurney, and J. A. Metz, Stage Structure Models Applied in Evolutionary Ecology, Biomathematics, pp.18-428, 1989.

R. Bence and R. M. Nisbet, Space-Limited Recruitment in Open Systems: The Importance of Time Delays, Ecology, vol.70, issue.5, pp.1434-1441, 1989.
DOI : 10.2307/1938202

A. L. Wilmot-smith, G. Nandy, and . Hornig, A Time Delay Model for Solar and Stellar Dynamos, The Astrophysical Journal, vol.652, issue.1, p.696, 2006.
DOI : 10.1086/508013

F. Crauste, Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model, Mathematical Biosciences and Engineering, vol.3, issue.2, pp.325-346, 2006.

. Crauste, A review on local asymptotic stability analysis for mathematical models of hematopoietic with delay and delay-dependent coefficients, Annals of the Tiberiu Popoviciu Seminar of functionnal equations, approximation and convexity, pp.121-143, 2011.

N. Young, An identity which implies Cohn's theorem on the zeros of a polynomial, Journal of Mathematical Analysis and Applications, vol.70, issue.1, pp.240-248, 1979.

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, p.249, 1969.
DOI : 10.1137/0307017

D. Hertz, E. J. Jury, and E. Zeheb, Stability independent and dependent of delay for delay differential systems, Journal of the Franklin Institute, vol.318, issue.3, pp.143-150, 1984.

X. G. Li, S. I. Niculescu, and A. Cela, Invariance properties for a class of quasipolynomials, Automatica, vol.50, issue.3, pp.50-890, 2014.

S. Ruan and J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dynamics of Continuous Discrete and Impulsive Systems Series A, pp.863-874, 2003.

L. V. Ahlfors, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, 1953.

X. Li, S. Niculescu, A. Çela, 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.

I. Boussaada and S. 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.61-1601, 2016.

K. Gu, D. Irofti, I. Boussaada, and S. I. 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

D. Irofti, K. Gu, I. Boussaada, and S. Niculescu, Migration of imaginary roots of multiplicity three and four under small deviation of two delays in time-delay systems, 2016 European Control Conference (ECC), 2016.

S. Niculescu, Delay effects on stability: a robust control approach, 2001.

S. Niculescu and W. Michiels, Stabilizing a Chain of Integrators Using Multiple Delays, IEEE Transactions on Automatic Control, pp.802-807, 2004.

S. Niculescu, P. Fu, and J. Chen, STABILITY SWITCHES AND REVERSALS OF LINEAR SYSTEMS WITH COMMENSURATE DELAYS: A MATRIX PENCIL CHARACTERIZATION, IFAC Proceedings Volumes, vol.38, issue.1, pp.406-411, 2005.

C. Jin, K. Gu, I. Boussaada, and S. I. Niculescu, Stability analysis of systems with delay-dependant coefficients: A two-parameter approach, 2017 American Control Conference (ACC), pp.2017-5726

C. Jin, S. I. Niculescu, I. Boussaada, and K. Gu, Stability Analysis of Control Systems subject to Delay-Difference Feedback, Proceeding of the 20th IFAC World Congress, 2017.

K. L. Cooke, P. Van-den-driessche, and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. BioI, pp.39-332, 1999.

F. G. Boese, Stability with Respect to the Delay: On a Paper of K. L. Cooke and P. van den Driessche, Journal of Mathematical Analysis and Applications, vol.228, issue.2, pp.293-321, 1998.

X. G. Li, S. Niculescu, A. Çela, 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.

X. G. Li, S. Niculescu, A. Cela, L. Zhang, and X. Li, A Frequency-Sweeping Framework for Stability Analysis of Time-Delay Systems, IEEE Transactions on Automatic Control, pp.1-1

J. Chen, P. Fu, S. 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.5564-5582, 2010.
DOI : 10.1137/080741707

J. Chen, P. Fu, S. 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.5583-5605, 2010.
DOI : 10.1137/080741719

Y. Kuang, Delay differential equations: with applications in population dynamics, 1993.

I. R. Epstein and L. Yin, Differential delay equations in chemical kinetics. Nonlinear models: The cross???shaped phase diagram and the Oregonator, The Journal of Chemical Physics, vol.79, issue.1, pp.244-254, 1991.

M. Szydlowski and A. Krawiec, The Kaldor???Kalecki Model of Business Cycle as a Two-Dimensional Dynamical System, Journal of Nonlinear Mathematical Physics, vol.89, issue.sup1, pp.1-266, 2001.

K. J. Astrom and T. Hagglund, The future of PID control, Control Engineering Practice, vol.9, issue.11, pp.1163-1175, 2000.

O. Garpinger, T. Hägglund, and &. K. Åström, Performance and robustness trade-offs in PID control, Journal of Process Control, vol.24, issue.5, pp.568-577, 2014.

F. Mazenc, S. Mondie, and S. I. Niculescu, Global asymptotic stabilization for chains of integrators with a delay in the input, IEEE Transactions on Automatic Control, vol.48, issue.1, pp.57-63, 2003.

K. Yamanaka and E. Shimemura, Use of multiple time-delays as controllers in IMC schemes, International Journal of Control, vol.82, issue.6, pp.1443-1451, 1993.

G. Miao, M. M. Peet, and K. Gu, Inversion of Separable Kernel Operators in Coupled Differential-Functional Equations and Application to Controller Synthesis, arXiv preprint, 2017.

A. Gahlawat and M. M. Peet, A Convex Sum-of-Squares Approach to Analysis, State Feedback and Output Feedback Control of Parabolic PDEs, IEEE Transactions on Automatic Control, pp.1636-1651, 2017.

L. Lapierre and B. Jouvencel, Robust Nonlinear Path-Following Control of an AUV, IEEE Journal of Oceanic Engineering, vol.33, issue.2, pp.89-102, 2008.

J. Chen, S. I. Niculescu, and P. Fu, Robust Stability of Quasi-Polynomials: Frequency-Sweeping Conditions and Vertex Tests, IEEE Transactions on Automatic Control, vol.53, issue.5, pp.1219-1234, 2008.

K. Gu, A further refinement of discretized Lyapunov functional method for the stability of time-delay systems, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), pp.3998-4003, 2001.

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.

K. Gu and M. Naghnaeian, Stability Crossing Set for Systems With Three Delays, IEEE Transactions on Automatic Control, pp.11-26, 2011.

K. Gu and S. Niculescu, Survey on Recent Results in the Stability and Control of Time-Delay Systems, Journal of Dynamic Systems, Measurement, and Control, vol.46, issue.2, pp.158-165, 2003.

]. K. Gu, V. L. Kharitonov, and &. J. Chen, Stability of time-delay systems A review of some subtleties of practical relevance for time-delay systems of neutral type, ISRN Applied Mathematics, vol.2012, pp.10-5402, 2003.

K. Gu, Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence Advances in Analysis and Control of Time-Delayed Dynamical Systems, New Jersey World Scientific, pp.1-19, 2013.

K. Gu, C. Jin, I. Boussaada, and S. I. Niculescu, Towards more general stability analysis of systems with delay-dependent coefficients, 2016 IEEE 55th Conference on Decision and Control (CDC), pp.3161-3166, 2016.

I. I. Delice and R. Sipahi, Delay-Independent Stability Test for Systems With Multiple Time-Delays, IEEE Transactions on Automatic Control, pp.963-972, 2012.

R. Sipahi and I. I. Delice, Advanced Clustering With Frequency Sweeping Methodology for the Stability Analysis of Multiple Time-Delay Systems, IEEE Transactions on Automatic Control, pp.467-472, 2011.

I. I. Delice and R. Sipahi, Advanced clustering with frequency sweeping (ACFS) methodology for the stability analysis of multiple time-delay systems, Proceedings of the 2010 American Control Conference, pp.5012-5017, 2010.

R. Sipahi and I. I. Delice, Extraction of 3D stability switching hypersurfaces of a time delay system with multiple fixed delays, Automatica, vol.45, issue.6, pp.1449-1454, 2009.

G. E. Collins, The calculation of multivariate polynomial resultants, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, pp.212-222

Z. V. Rekasius, A stability test for systems with delays, Proc. Joint Autom. Control Conf, 1980.

J. K. Hale, F. I. Ettore, and F. S. Petersen, Stability in linear delay equations, Journal of Mathematical Analysis and Applications, vol.105, issue.2, pp.533-555, 1985.

G. Tallman and O. Smith, Analog study of dead-beat posicast control, IRE Transactions on Automatic Control, pp.14-21, 1958.

O. Smith, A Controller to Overcome Dead Time, Indian Scientist Association in Japan, vol.6, issue.2, pp.28-33, 1959.

I. Suh and Z. Bien, Proportional minus delay controller, IEEE Transactions on Automatic Control, vol.24, issue.2, pp.370-372, 1979.

N. Olgac, A. F. Ergenc, and R. Sipahi, ???Delay Scheduling???: A New Concept for Stabilization in Multiple Delay Systems, Modal Analysis, vol.15, issue.3, pp.1159-1172, 2005.
DOI : 10.1109/70.768190

R. Sipahi and N. Olgac, Active Vibration Suppression With Time Delayed Feedback, Journal of Vibration and Acoustics, vol.29, issue.3, pp.384-388, 2003.
DOI : 10.1115/1.1569942

A. Ramírez, R. Garrido, R. Sipahi, and S. Mondié, On Delay-Based Control of Low-Order LTI Systems: a Simple Alternative to PI/PID Controllers Under Noisy Measurements, IFAC-PapersOnLine, vol.49, issue.10, pp.188-193, 2016.

A. Ramírez, S. Mondié, R. Garrido, and R. Sipahi, Design of Proportional-Integral-Retarded (PIR) Controllers for Second-Order LTI Systems, IEEE Transactions on Automatic Control, vol.61, issue.6, pp.1688-1693, 2016.

A. Ramírez, R. Sipahi, S. Mondié, and R. Garrido, Design of Maximum Decay Rate for SISO Systems with Delayed Output Feedback Using Elimination Theory, IEEE Transactions on Automatic Control, vol.82, p.86, 2015.

A. Ramirez, R. Sipahi, S. Mondié, and R. Garrido, An Analytical Approach to Tuning of Delay-Based Controllers for LTI-SISO Systems, SIAM Journal on Control and Optimization, vol.55, issue.1, pp.397-412, 2017.
DOI : 10.1137/15M1050999

R. Sipahi, F. M. Atay, and S. Niculescu, Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers, SIAM Journal on Applied Mathematics, vol.68, issue.3, pp.738-759, 2007.
DOI : 10.1137/060673813

P. Zítek, F. Jaromír, and V. Tomá?stomá?s, ULTIMATE-FREQUENCY BASED THREE-POLE DOMINANT PLACEMENT IN DELAYED PID CONTROL LOOP, IFAC Proceedings Volumes, vol.45, issue.14, pp.150-155, 2012.

K. Pyragas, Continuous control of chaos by self-controlling feedback, Physics Letters A, vol.170, issue.6, pp.421-428, 1992.

A. G. Ulsoy, Time-Delayed Control of SISO Systems for Improved Stability Margins, 2017 American Control Conference (ACC), pp.41014-5127, 2015.
DOI : 10.1115/1.4028528

M. M. Peet, A. Papachristodoulou, and S. Lall, Positive Forms and Stability of Linear Time-Delay Systems, SIAM Journal on Control and Optimization, vol.47, issue.6, pp.3237-3258, 2009.
DOI : 10.1137/070706999

M. M. Peet, LMI parametrization of Lyapunov functions for infinite-dimensional systems: A framework, 2014 American Control Conference, pp.359-366

A. Seuret and F. Gouaisbaut, Complete Quadratic Lyapunov functionals using Bessel-Legendre inequality, 2014 European Control Conference (ECC), pp.448-453

E. Fridman, Introduction to time-delay systems: Analysis and control, 2014.

V. Kharitonov, Time-delay systems: Lyapunov functionals and matrices, 2012.

S. A. Campbell, Calculating Centre Manifolds for Delay Differential Equations Using Maple TM Delay differential equations, pp.1-24, 2009.

C. Heckman, K. Jakob, and R. Richard, Center Manifold Reduction of the Hopf-Hopf Bifurcation in a Time Delay System, ESAIM: Proceedings, pp.57-65, 2013.

M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and adaptive control design, 1995.

P. Kokotovi´ckokotovi´c and M. Arcak, Constructive nonlinear control: a historical perspective, Automatica, vol.37, issue.5, pp.637-662, 2001.

F. Mazenc and L. Praly, Adding an integration and global asymptotic stabilization of feedforward systems, Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp.1559-1578, 1996.

F. Mazenc and M. Malisoff, New control design for bounded backstepping under input delays, Automatica, vol.66, pp.48-55, 2016.

F. Mazenc and M. Malisoff, Asymptotic stabilization for feedforward systems with delayed feedbacks, Automatica, vol.49, issue.3, pp.780-787, 2013.

M. Jankovic, Cross-Term Forwarding for Systems With Time Delay, IEEE Transactions on Automatic Control, vol.54, issue.3, pp.498-511, 2009.

T. D. Gillespie, Vehicle Dynamics, 1997.

P. Lancaster and M. Tismenetsky, The theory of matrices: with applications, 1985.

J. A. Cook and B. K. Powell, Modeling of an internal combustion engine for control analysis, IEEE Control Systems Magazine, pp.20-26, 1988.
DOI : 10.1109/37.7726

K. Youcef-toumi and S. Reddy, Stability analysis of time delay control with application to high speed magnetic bearings, ASME Winter Annual Meeting, p.1, 1990.

N. Olgac and B. T. Holm-hansen, A Novel Active Vibration Absorption Technique: Delayed Resonator, Journal of Sound and Vibration, vol.176, issue.1, pp.93-104, 1994.

K. Pyragas, Control of chaos via extended delay feedback, Physics Letters A, vol.206, issue.5-6, pp.323-330, 1995.

A. Halanay and V. Rasvan, Stability radii for some propagation models, IMA Journal of Mathematical Control and Information, vol.14, issue.1, pp.95-107, 1997.

. Gábor and . Stépán, Retarded dynamical systems: stability and characteristic functions, Longman Scientific & Technical, 1989.

Q. Xu, G. Stepan, and Z. Wang, Delay-dependent stability analysis by using delay-independent integral evaluation, Automatica, vol.70, pp.153-157, 2016.

T. Insperger and G. Stépán, Semi-discretization for time-delay systems: stability and engineering applications, 2011.

C. Foley and M. C. Mackey, Mathematical model for G-CSF administration after chemotherapy, Journal of Theoretical Biology, vol.257, issue.1, pp.27-44, 2009.

V. Rasvan, Absolute stability of time lag control systems (in Romanian)

W. Djema, F. Mazenc, C. Bonnet, J. Clairambault, and . Hirsch, Stability of a delay system coupled to a differential-difference system describing the coexistence of ordinary and mutated hematopoietic stem cells, 2016 IEEE 55th Conference on Decision and Control (CDC), 2016.

A. G. Mckendrick, Applications of Mathematics to Medical Problems, Proceedings of the Edinburgh Mathematical Society 44, pp.98-130, 1925.
DOI : 10.1038/104660a0

M. Adimy, A. Chekroun, and T. M. Touaoula, Age-Structured and Delay Differential- Difference Model Of Hematopoietic Stem Cell Dynamics Discrete And Continuous Dynamical Systems Series B, pp.2765-2791, 2015.