V. I. Zubov, Methods of A.M. Lyapunov and Their Applications, 1964.

W. Hahn, Stability of Motion, 1967.
DOI : 10.1007/978-3-642-50085-5

V. Zubov, On systems of ordinary differential equations with generalized homogenous right-hand sides, Izvestia vuzov. Mathematica, vol.1, pp.80-88, 1958.

H. Hermes, Nilpotent Approximations of Control Systems and Distributions, SIAM Journal on Control and Optimization, vol.24, issue.4, p.731, 1986.
DOI : 10.1137/0324045

L. Rosier, Homogeneous Lyapunov function for homogeneous continuous vector field, Systems & Control Letters, vol.19, issue.6, pp.467-473, 1992.
DOI : 10.1016/0167-6911(92)90078-7

G. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv f??r Matematik, vol.13, issue.1-2, pp.161-207, 1975.
DOI : 10.1007/BF02386204

V. V. Khomenuk, On systems of ordinary differential equations with generalized homogenous right-hand sides, Izvestia vuzov. Mathematica, vol.3, issue.22, pp.157-164, 1961.

L. Rosier, Etude de quelques problemes de stabilization, 1993.

M. Kawski, GEOMETRIC HOMOGENEITY AND STABILIZATION, Proc. IFAC Nonlinear Control Symposium, pp.164-169, 1995.
DOI : 10.1016/B978-0-08-042371-5.50030-7

A. Bacciotti and L. Rosier, Lyapunov Functions and Stability in Control Theory, 2001.

S. P. Bhat and D. S. Bernstein, Geometric homogeneity with applications to finite-time stability, Mathematics of Control, Signals, and Systems, vol.17, issue.2, pp.101-127, 2005.
DOI : 10.1007/s00498-005-0151-x

Y. Orlov, Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems, SIAM Journal on Control and Optimization, vol.43, issue.4, pp.1253-1271, 2005.
DOI : 10.1137/S0363012903425593

A. Levant, Homogeneity approach to high-order sliding mode design, Automatica, vol.41, issue.5, pp.823-830, 2005.
DOI : 10.1016/j.automatica.2004.11.029

V. Andrieu, L. Praly, and A. Astolfi, Homogeneous Approximation, Recursive Observer Design, and Output Feedback, SIAM Journal on Control and Optimization, vol.47, issue.4, pp.1814-1850, 2008.
DOI : 10.1137/060675861
URL : https://hal.archives-ouvertes.fr/hal-00362707

V. Haimo, Finite Time Controllers, SIAM Journal on Control and Optimization, vol.24, issue.4, pp.760-770, 1986.
DOI : 10.1137/0324047

A. Polyakov, D. Efimov, and W. Perruquetti, Finite-time Stabilization Using Implicit Lyapunov Function Technique, 9th Symposium on Nonlinear Control Systems, pp.140-145
DOI : 10.3182/20130904-3-FR-2041.00043
URL : https://hal.archives-ouvertes.fr/hal-00844386

W. Perruquetti, T. Floquet, and E. Moulay, Finite-Time Observers: Application to Secure Communication, European Control Conference (ECC), pp.356-360, 2008.
DOI : 10.1109/TAC.2007.914264
URL : https://hal.archives-ouvertes.fr/inria-00176758

E. Ryan, Universal stabilization of a class of nonlinear systems with homogeneous vector fields, Systems & Control Letters, vol.26, issue.3, pp.177-184, 1995.
DOI : 10.1016/0167-6911(95)00013-Y

Y. Hong, H??? control, stabilization, and input???output stability of nonlinear systems with homogeneous properties, Automatica, vol.37, issue.6, pp.819-829, 2001.
DOI : 10.1016/S0005-1098(01)00027-9

E. Bernuau, A. Polyakov, D. Efimov, and W. Perruquetti, Verification of ISS, iISS and IOSS properties applying weighted homogeneity, Systems & Control Letters, vol.62, issue.12, pp.1159-1167, 2013.
DOI : 10.1016/j.sysconle.2013.09.004
URL : https://hal.archives-ouvertes.fr/hal-00877148

D. Efimov and W. Perruquetti, Oscillations Conditions in Homogenous Systems, Proc. IFAC NOLCOS Symp, pp.1379-1384, 2010.
DOI : 10.3182/20100901-3-IT-2016.00101
URL : https://hal.archives-ouvertes.fr/hal-00561003

R. Sepulchre and D. Aeyels, Homogeneous Lyapunov functions and necessary conditions for stabilization, Mathematics of Control, Signals, and Systems, vol.3, issue.No. 3, pp.34-58, 1996.
DOI : 10.1007/BF01211517

H. Nakamura, Positive Definiteness of Generalized Homogeneous Functions, 9th Symposium on Nonlinear Control Systems, pp.4-6, 2013.
DOI : 10.3182/20130904-3-FR-2041.00150

A. Polyakov, D. Efimov, and W. Perruquetti, Finite-time and fixed-time stabilization: Implicit Lyapunov function approach, Automatica, vol.51, issue.1, pp.332-340, 2015.
DOI : 10.1016/j.automatica.2014.10.082
URL : https://hal.archives-ouvertes.fr/hal-01098099

P. Benilan and M. Crandall, Regularizing effects of homogeneous evolution equations, Contributions to Analysis and Geometry, 1981.

J. A. Sanders and J. P. Wang, On the Integrability of Homogeneous Scalar Evolution Equations, Journal of Differential Equations, vol.147, issue.2, pp.410-434, 1998.
DOI : 10.1006/jdeq.1998.3452

V. Sokolov and T. Wolf, Classification of integrable polynomial vector evolution equations, Journal of Physics A: Mathematical and General, vol.34, issue.49, 2001.
DOI : 10.1088/0305-4470/34/49/327

V. Perrollaz and L. Rosier, Finite-Time Stabilization of $2\times2$ Hyperbolic Systems on Tree-Shaped Networks, SIAM Journal on Control and Optimization, vol.52, issue.1, pp.143-163, 2014.
DOI : 10.1137/130910762

M. Ablowitz and P. Clarkson, Solutions, Nonlinear Evolution Equations and Inverse Scattering, 1991.

S. Zheng, Nonlinear Evolution Equations, 2004.
DOI : 10.1201/9780203492222

V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces, 2010.
DOI : 10.1007/978-1-4419-5542-5

L. Husch, Topological characterization of the dilation and the translation in Frechet spaces, Mathematische Annalen, vol.128, issue.2, pp.1-5, 1970.
DOI : 10.1007/BF01349965

L. Auslander, L. Green, and F. Hahn, Flows on homogeneous spaces, 1963.

E. Bernuau, D. Efimov, W. Perruquetti, and A. Polyakov, On homogeneity and its application in sliding mode control, Journal of the Franklin Institute, vol.351, issue.4, pp.1866-1901, 2014.
DOI : 10.1016/j.jfranklin.2014.01.007
URL : https://hal.archives-ouvertes.fr/hal-00942326

J. Coron, B. Andrea-novel, and G. Bastin, A Strict Lyapunov Function for Boundary Control of Hyperbolic Systems of Conservation Laws, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.2-11, 2007.
DOI : 10.1109/TAC.2006.887903

L. Dalecky and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, 1974.

E. Roxin, On finite stability in control systems, Rendiconti del Circolo Matematico di Palermo, pp.273-283, 1966.
DOI : 10.1007/BF02844106

S. Bhat and D. Bernstein, Finite-Time Stability of Continuous Autonomous Systems, SIAM Journal on Control and Optimization, vol.38, issue.3, pp.751-766, 2000.
DOI : 10.1137/S0363012997321358

Y. Shang, D. Liu, and G. Xu, Super-stability and the spectrum of one-dimensional wave equations on general feedback controlled networks, IMA Journal of Mathematical Control and Information, vol.31, issue.1, pp.73-99, 2014.
DOI : 10.1093/imamci/dnt003

E. Sabinina, A class of non-linear degenerating parabolic equations, Soviet Methematics Doklady, vol.148, pp.495-498, 1962.

J. Berryman and C. Holland, Stability of the separable solution for fast diffusion Archive for Rational Mechanics and Analysis, pp.379-388, 1980.

M. Bonforte, G. Grillo, and J. L. Vazquez, Behaviour near extinction for the Fast Diffusion Equation on bounded domains, Journal de Math??matiques Pures et Appliqu??es, vol.97, issue.1, pp.1-38, 2012.
DOI : 10.1016/j.matpur.2011.03.002

V. A. Galaktionov and J. L. Vazquez, Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations, Archive for Rational Mechanics and Analysis, vol.93, issue.3, pp.225-244, 1995.
DOI : 10.1007/BF00383674