D. Eduardo and . Sontag, Smooth stabilization implies coprime factorization, IEEE Transactions on Automatic Control, vol.34, issue.4, pp.435-443, 1989.

D. Eduardo and . Sontag, Comments on integral variants of ISS, Systems & Control Letters, vol.34, issue.1-2, pp.93-100, 1998.

M. Arcak and P. Kokotovi´ckokotovi´c, Nonlinear observers: a circle criterion design and robustness analysis, Automatica, vol.37, issue.12, pp.1923-1930, 2001.

R. Freeman, V. Petar, and . Kokotovic, Robust nonlinear control design: state-space and Lyapunov techniques, 2008.

A. Chaillet, D. Angeli, and H. Ito, Combining iISS and ISS with respect to small inputs: the strong iISS property, IEEE Transactions on Automatic Control, vol.59, issue.9, pp.2518-2524, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01103296

A. Chaillet, D. Angeli, and H. Ito, Strong iISS is preserved under cascade interconnection, Automatica, vol.50, issue.9, pp.2424-2427, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01103301

D. Eduardo, Y. Sontag, and . Wang, New characterizations of input-tostate stability, IEEE Transactions on Automatic Control, vol.41, issue.9, pp.1283-1294, 1996.

S. Dashkovskiy, M. Görges, and L. Naujok, Local inputto-state stability of production networks, Dynamics in logistics, pp.79-89, 2011.

D. Angeli, Input-to-state stability of pd-controlled robotic systems, Automatica, vol.35, issue.7, pp.1285-1290, 1999.

M. Arcak, D. Angeli, and E. Sontag, A unifying integral iss framework for stability of nonlinear cascades, SIAM Journal on Control and Optimization, vol.40, issue.6, pp.1888-1904, 2002.

D. Eduardo, Y. Sontag, and . Wang, On characterizations of the inputto-state stability property, Systems & Control Letters, vol.24, issue.5, pp.351-359, 1995.

D. Angeli and D. Efimov, On input-to-state stability with respect to decomposable invariant sets, Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, pp.5897-5902, 2013.

D. Angeli and D. Efimov, Characterizations of input-to-state stability for systems with multiple invariant sets, IEEE Transactions on Automatic Control, pp.1-13, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01136819

D. Efimov, R. Ortega, and J. Schiffer, ISS of multistable systems with delays: application to droop-controlled inverterbased microgrids, American Control Conference (ACC), pp.4664-4669, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01140346

D. Efimov, J. Schiffer, and R. Ortega, Robustness of delayed multistable systems with application to droopcontrolled inverter-based microgrids, International Journal of Control, vol.89, issue.5, pp.909-918, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01211454

W. Hahn, H. Hans, H. Hosenthien, and . Lehnigk, Theory and application of Lyapunov's direct method, 1963.

W. Hahn, Stability of motion, vol.138, 1967.

P. Sanjay, D. S. Bhat, and . Bernstein, Geometric homogeneity with applications to finite-time stability, Mathematics of Control, Signals and Systems, vol.17, issue.2, pp.101-127, 2005.

A. Bacciotti and L. Rosier, Liapunov functions and stability in control theory, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00139067

J. Coron, Control and nonlinearity. Number 136, 2007.

D. Efimov and W. Perruquetti, Oscillations conditions in homogenous systems, 8th IFAC Symposium on Nonlinear Control Systems, pp.1379-1384, 2010.
DOI : 10.3182/20100901-3-it-2016.00101

URL : https://hal.archives-ouvertes.fr/hal-00561003

E. Bernuau, D. Efimov, W. Perruquetti, and A. Polyakov, On an extension of homogeneity notion for differential inclusions, Control Conference ECC, pp.2204-2209, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00801818

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

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

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

. Ep-ryan, Universal stabilization of a class of nonlinear systems with homogeneous vector fields, Systems & Control Letters, vol.26, issue.3, pp.177-184, 1995.

Z. Vladimir-ivanovich, On systems of ordinary differential equations with generalized homogenous right-hand sides, Izvestia Vuzov. mathematica, vol.1, pp.80-88, 1958.

E. Roxin, On finite stability in control systems, Rendiconti del Circolo Matematico di Palermo, vol.15, issue.3, pp.273-283, 1966.

V. I. Korobov, A general approach to synthesis problem, Doklady Academii Nauk SSSR, vol.248, pp.1051-1063, 1979.

P. Sanjay, D. Bhat, and . Bernstein, Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization, vol.38, issue.3, pp.751-766, 2000.

W. Perruquetti, T. Floquet, and E. Moulay, Finitetime observers: application to secure communication, IEEE Transactions on Automatic Control, vol.53, issue.1, pp.356-360, 2008.
DOI : 10.1109/tac.2007.914264

URL : https://hal.inria.fr/inria-00176758/document

Y. Hong, Z. Jiang, and G. Feng, Finite-time input-to-state stability and applications to finite-time control. IFAC Proceedings Volumes, vol.41, pp.2466-2471, 2008.

. Sn-dashkovskiy, V. Denis, E. D. Efimov, and . Sontag, Input to state stability and allied system properties. Automation and Remote Control, vol.72, p.1579, 2011.

E. Moulay and W. Perruquetti, Finite time stability and stabilization of a class of continuous systems, Journal of Mathematical Analysis and Applications, vol.323, issue.2, pp.1430-1443, 2006.

A. Polyakov, D. Efimov, E. Fridman, and W. Perruquetti, On homogeneous distributed parameter systems, IEEE Transactions on Automatic Control, vol.61, issue.11, pp.3657-3662, 2016.
DOI : 10.1109/tac.2016.2525925

URL : https://hal.archives-ouvertes.fr/hal-01318134

A. Polyakov, J. Coron, and L. Rosier, On homogeneous finite-time control for linear evolution equation in Hilbert space, IEEE Transactions on Automatic Control, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01695475

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

D. Efimov and W. Perruquetti, On conditions of oscillations and multi-homogeneity. Mathematics of Control, Signals, and Systems, vol.28, p.3, 2016.
DOI : 10.1007/s00498-015-0157-y

URL : https://hal.archives-ouvertes.fr/hal-01223154

D. Efimov, R. Ushirobira, J. A. Moreno, and W. Perruquetti, Homogeneous lyapunov functions: from converse design to numerical implementation, SIAM Journal on Control and Optimization, vol.56, issue.5, pp.3454-3477, 2018.
DOI : 10.1137/17m113753x

URL : https://hal.archives-ouvertes.fr/hal-01851761

A. Polyakov, Sliding mode control design using canonical homogeneous norm, International Journal of Robust and Nonlinear Control, 2018.
DOI : 10.1002/rnc.4058

URL : https://hal.archives-ouvertes.fr/hal-01697797

A. Polyakov, Quadratic-like stability of nonlinear homogeneous systems, 56th IEEE Conference on Decision and Control, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01525252

R. Lozi, Secure communications via chaotic synchronization in Chua's circuit and Bonhoeffer-Van der Pol equation: numerical analysis of the errors of the recovered signal, Circuits and Systems, 1995. ISCAS'95, vol.1, pp.684-687, 1995.

M. Itoh, H. Murakami, and L. O. Chua, Performance of Yamakawa's chaotic chips and Chua's circuits for secure communications, Circuits and Systems, 1994. ISCAS'94, vol.6, pp.105-108, 1994.