A. Polyakov, Characterization of finite/fixed-time stability of evolution inclusions, Conference on Decision and Control, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02278740

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

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

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

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

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

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

Y. Orlov, Finite time stability and robust control synthesis of uncertain switched systems, SIAM Journal of Control and Optimization, vol.43, issue.4, pp.1253-1271, 2005.

V. Andrieu, L. Praly, and A. Astolfi, 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

V. Haimo, Finite time controllers, SIAM Journal of Control and Optimization, vol.24, issue.4, pp.760-770, 1986.

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, J. Coron, and L. Rosier, Boundary finite-time feedback design for heat equation, IFAC World Congress, 2017.

, 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.

N. Espitia, A. Polyakov, D. Efimov, and W. Perruquetti, Boundary time-varying feedbacks for fixed-time stabilization of constantparameter reaction-diffusion systems, Automatica, vol.103, issue.5, pp.398-407, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01962662

E. Moulay and W. Perruquetti, Finite-time stability of differential inclusions, IMA Journal Mathematical Control and Information Sciences, vol.22, issue.4, pp.465-475, 2005.

F. Lopez-ramirez, D. Efimov, A. Polyakov, and W. Perruquetti, On necessary and sufficient conditions for fixed-time stability of continuous autonomous systems, European Control Conference (ECC), pp.197-200, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01755079

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

B. Driver, Analysis Tools with Applications, 2003.

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

N. Papageorgiou, A stability result for differential inclusions in banach spaces*, Journal of Mathematical Analysis and Applications, vol.118, pp.232-246, 1986.

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

A. M. Lyapunov, The general problem of the stability of motion, 1992.

A. Polyakov and L. Fridman, Stability notions and Lyapunov functions for sliding mode control systems, Journal of The Franklin Institute, vol.351, issue.4, pp.1831-1865, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00942319

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

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

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.

K. Deimling, Multivariable Differential Equations, 1992.

A. Pisano, Y. Orlov, and E. Usai, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques, SIAM Journal on Control and Optimization, vol.49, issue.2, pp.363-382, 2011.

A. Polyakov, On homogeneous Lyapunov function theorem for evolution equations, IFAC World Congress, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02495818

, Generalized Homogeneity in Systems and Control, 2020.