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

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

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.
URL : https://hal.archives-ouvertes.fr/hal-00942326

S. Bhat and D. Bernstein, Finite time stability of continuous autonomous systems, SIAM J. Control Optim, vol.38, issue.3, pp.751-766, 2000.

F. H. Clarke, Y. S. Ledyaev, and R. Stern, Asymptotic stability and smooth Lyapunov functions, Journal of differential Equations, vol.149, pp.69-114, 1998.

J. M. Coron and L. Praly, Adding an integrator for the stabilization problem, Systems & Control Letters, vol.17, issue.2, pp.89-104, 1991.

K. Deimling, Multivariable Differential Equations, 1992.

B. Driver, Analysis Tools with Applications, 2003.

K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equationsarameter, 2000.

V. Fischer and M. Ruzhansky, Quantization on Nilpotent Lie Groups, 2016.

G. Folland, Subelliptic estimates and function spaces on nilpotent lie groups, Arkiv for Matematik, vol.13, issue.1-2, pp.161-207, 1975.

H. Hermes, Nilpotent approximations of control systems and distributions, SIAM Journal of Control and Optimization, vol.24, issue.4, p.731, 1986.

B. Jacob, A. Mironchenko, J. Partington, and F. Wirth, Remarks on input-to-state stability and noncoercive lyapunov functions, 2018 IEEE Conference on Decision and Control (CDC), pp.4803-4808, 2018.

I. Karafyllis and M. Krstic, Input-to-State Stability for PDEs, 2018.

M. Kawski, Homogeneous stabilizing feedback laws, Control Theory and Advanced Technology, vol.6, issue.4, pp.497-516, 1990.

M. Kawski, Families of dilations and asymptotic stability, Analysis of Controlled Dynamical Systems, pp.285-294, 1991.

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

S. Krein and M. Khazan, Differential equations in a banach space, Journal of Soviet Mathematics, vol.30, issue.3, pp.2154-2239, 1985.

F. Lopez-ramirez, A. Polyakov, D. Efimov, and W. Perruquetti, Finite-time and fixed-time observer design: Implicit Lyapunov function approach, Automatica, vol.87, issue.1, pp.52-60, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01622356

A. Majda, Disappearing solutions for the dissipative wave equation, Indiana University Mathematics Journal, vol.24, issue.12, pp.1119-1133, 1975.

A. Mironchenko and F. Wirth, Noncoercive lyapunov functions for infinite-dimensional systems, Journal of Differential Equations, 2019.

H. Nakamura, Y. Yamashita, and H. Nishitani, Smooth Lyapunov functions for homogeneous differential inclusions, Proceedings of the 41st SICE Annual Conference, pp.1974-1979, 2002.

I. Natanson, Theory of functions of a real variable, 1955.

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1983.

V. Perrollaz and L. Rosier, Finite-time stabilization of 2x2 hyperbolic systems on tree-shaped networks, SIAM Journal of Control and Optimization, vol.52, issue.1, pp.143-163, 2014.

A. Polyakov, Sliding mode control design using canonical homogeneous norm, International Journal of Robust and Nonlinear Control, vol.29, issue.3, pp.682-701, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01697797

A. Polyakov, Characterization of finite/fixedtime stability of evolution inclusions, Conference on Decision and Control, 2019.

A. Polyakov, Generalized Homogeneity in Systems and Control, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02426338

A. Polyakov, J. M. Coron, and L. Rosier, On homogeneous finite-time control for linear evolution equation in hilbert space, IEEE Transactions on Automatic Control, vol.63, issue.9, pp.3143-3150, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01695475

A. Polyakov, D. Efimov, E. Fridman, and W. Perruquetti, On homogeneous distributed parameters equations, IEEE Transactions on Automatic Control, issue.11, pp.3657-3662, 2016.

C. Prieur and F. Mazenc, Iss-lyapunov functions for time-varying hyperbolic systems of balance laws, Mathematics of Control, Signals, and Systems, vol.24, issue.1, pp.111-134, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00682443

L. Rosier, Homogeneous Lyapunov function for homogeneous continuous vector field, Systems & Control Letters, vol.19, pp.467-473, 1992.

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

E. Ryan, Universal stabilization of a class of nonlinear systems with homogeneous vector fields, Systems & Control Letters, vol.26, pp.177-184, 1995.

J. Tabor, Generalized differential inclusions in banach spaces, Set-Valued Analysis, vol.14, pp.121-148, 2006.

V. I. Zubov, Methods of A.M. Lyapunov and Their Applications. Noordhoff, Leiden (Translated from Russian: V.I. Zubov, Metody Lyapunova i ih primenenie, 1957.

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