L. Bao, S. Fei, and L. Yu, Exponential stability of linear distributed parameter switched systems with time-delay, Journal of Systems Science and Complexity, vol.25, issue.3, pp.263-275, 2014.
DOI : 10.1016/j.aml.2011.07.013

R. Curtain and H. Zwart, An introduction to infinitedimensional linear systems theory, 1995.

E. Fridman, Stability of Systems With Uncertain Delays: A New ???Complete??? Lyapunov???Krasovskii Functional, IEEE Transactions on Automatic Control, vol.51, issue.5, pp.885-890, 2006.
DOI : 10.1109/TAC.2006.872769

E. Fridman and S. I. 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, U. Shaked, and K. Liu, New conditions for delay-derivative-dependent stability, Automatica, vol.45, issue.11, pp.2723-2727, 2009.
DOI : 10.1016/j.automatica.2009.08.002

K. Gu, V. L. Kharitonov, and J. Chen, Stability of time-delay systems, Birkhäuser, 2003.
DOI : 10.1007/978-1-4612-0039-0

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

J. W. Hagood and B. S. Thomson, Recovering a Function from a Dini Derivative, The American Mathematical Monthly, vol.113, issue.1, pp.34-46, 2006.
DOI : 10.2307/27641835

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

F. Hante and M. Sigalotti, Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces, SIAM Journal on Control and Optimization, vol.49, issue.2, pp.752-770, 2011.
DOI : 10.1137/100801561

URL : https://hal.archives-ouvertes.fr/hal-00489958

L. Hetel, J. Daafouz, and C. Iung, Equivalence between the Lyapunov???Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems, Nonlinear Analysis: Hybrid Systems, vol.2, issue.3, pp.697-705, 2008.
DOI : 10.1016/j.nahs.2007.11.003

URL : https://hal.archives-ouvertes.fr/hal-00323912

W. Huang, Generalization of Liapunov's theorem in a linear delay system, Journal of Mathematical Analysis and Applications, vol.142, pp.83-94, 1989.

I. Karafyllis, Lyapunov theorems for systems described by retarded functional differential equations. Nonlinear Analysis: Theory, Methods & Applications, pp.590-617, 2006.
DOI : 10.1109/cdc.2005.1582909

URL : http://arxiv.org/abs/math/0506368

I. Karafyllis, P. Pepe, and Z. Jiang, Global Output Stability for Systems Described by Retarded Functional Differential Equations: Lyapunov Characterizations, European Journal of Control, vol.14, issue.6, pp.516-536, 2008.
DOI : 10.3166/ejc.14.516-536

V. L. Kharitonov and A. P. Zhabko, Lyapunov???Krasovskii approach to the robust stability analysis of time-delay systems, Automatica, vol.39, issue.1, pp.15-20, 2003.
DOI : 10.1016/S0005-1098(02)00195-4

J. C. Lillo, Oscillatory solutions of the equation y???(x) = m(x)y(x ??? n(x)), Journal of Differential Equations, vol.6, issue.1, pp.1-35, 1969.
DOI : 10.1016/0022-0396(69)90114-4

F. Mazenc, S. I. Niculescu, and M. Krstic, Lyapunov???Krasovskii functionals and application to input delay compensation for linear time-invariant systems, Automatica, vol.48, issue.7, pp.481317-1323, 2012.
DOI : 10.1016/j.automatica.2012.04.002

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

A. D. Myshkis, On solutions of linear homogeneous differential equations of the first order of stable type with a retarded argument (in Russian), Mat. Sb, issue.703, pp.28641-658, 1951.

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

P. Pepe and I. Karafyllis, Converse Lyapunov???Krasovskii theorems for systems described by neutral functional differential equations in Hale's form, International Journal of Control, vol.53, issue.2, pp.232-243, 2013.
DOI : 10.1109/TAC.2008.928340

J. P. 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

]. A. Sasane, Stability of switching infinite-dimensional systems, Automatica J. IFAC, vol.41, issue.1, pp.75-78, 2005.
DOI : 10.1016/j.automatica.2004.07.013

R. Triggiani, A sharp result on the exponential operator-norm decay of a family of strongly continuous semigroups, Semigroup Forum, vol.3, issue.1, pp.387-395, 1994.
DOI : 10.1007/BF02573499