H. Ahmed, R. Ushirobira, D. Efimov, and W. Perruquetti, Robust synchronization for multistable systems, IEEE Transactions on Automatic Control, issue.6, pp.1625-1630, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01185112

D. Angeli, An almost global notion of input-to-state stability, IEEE Trans. Automatic Control, vol.49, pp.866-874, 2004.

D. Angeli and D. Efimov, Characterization of input-to-state stability for systems with multiple invariant sets, IEEE Transactions on Automatic Control, vol.60, pp.3242-3256, 2015.

D. Angeli, J. Ferrell, and E. Sontag, Detection of multistability, bifurcations and hysteresis in a large class of biological positive-feedback systems, Proc. Natl. Acad. Sci. USA, vol.101, pp.1822-1827, 2004.

D. Angeli, E. D. Sontag, and Y. Wang, A characterization of integral input-to-state stability, IEEE Transactions on Automatic Control, vol.45, pp.1082-1097, 2000.

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

Y. A. Astrov, A. L. Fradkov, and P. Y. Guzenko, Control of a noise-induced transition in a nonlinear dynamical system, Physical Review, vol.77, pp.1-7, 2008.

F. N. Barroso, R. Ushirobira, D. Efimov, and A. L. Fradkov, On robust stability of multistable passive systems, pp.1683-1688, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02418552

M. Chaves, T. Eissing, and F. Allgöwer, Bistable biological systems: A characterization through local compact input-to-state stability, IEEE Transactions on Automatic Control, vol.45, pp.87-100, 2008.

S. N. Dashkovskiy, D. Efimov, and E. D. Sontag, Input to state stability and allied system properties. Automation and Remote Control, vol.72, pp.1579-1614, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00639491

D. Dudkowski, S. Jafari, T. Kapitaniak, N. V. Kuznetsov, G. A. Leonov et al., Hidden attractors in dynamical systems, Physics Reports, vol.637, pp.1-50, 2016.

D. Efimov, Passivity and input-to-state stability of nonlinear systems, IFAC Proceedings Volumes, vol.39, pp.285-290, 2006.

D. Efimov, Global lyapunov analysis of multistable nonlinear systems, SIAM Journal on Control and Optimization, vol.50, issue.5, pp.3132-3154, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00745623

D. Efimov and A. Fradkov, Adaptive input-to-output stabilization of nonlinear systems, International Journal of Adaptive Control and Signal Processing, vol.22, pp.949-967, 2008.

D. Efimov, J. Schiffer, N. Barabanov, and R. Ortega, A relaxed characterization of iss for periodic systems with multiple invariant sets, European Journal of Control, vol.37, pp.1-7, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01351139

G. Enciso and E. Sontag, Monotone systems under positive feedback: multistability and a reduction theorem, Systems & Control Lett, vol.54, pp.159-168, 2005.

F. Forni and R. Sepulchre, Differential analysis of nonlinear systems: Revisiting the pendulum example, Proc. 53rd ieee conference on decision and control, pp.3848-3859, 2014.

P. Forni and D. Angeli, Input-to-state-stability for cascade systems with multiple invariant sets, Systems & Control Letters, vol.98, pp.97-110, 2016.

P. Forni and D. Angeli, Output-to-state stability for systems on manifolds with multiple invariant sets, IEEE Conference on Decision and Control, vol.55, pp.453-458, 2016.

P. Forni and D. Angeli, Characterization of integral input-to-state stability for systems with multiple invariant sets, IEEE Transactions on Automatic Control, vol.62, pp.3729-3743, 2017.

A. Fradkov, Cybernetical physics: From control of chaos to quantum control, 2007.

J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, vol.42, 1983.

C. Hayachi, Nonlinear oscillations in physical systems, 1964.

D. Hill and P. Moylan, Dissipative dynamical systems: Basic input-output and state properties, Journal of the Franklin Institute, vol.309, pp.327-357, 1980.

J. H. Kim, H. Maurer, Y. A. Astrov, M. Bode, and H. G. Purwinst, High-speed switch-on of a semiconductor gas discharge image converter using optimal control methods, Journal of Computational Physics, vol.170, pp.395-414, 2001.

M. Laurent and N. Kellershohn, Multistability: a major means of differentiation and evolution in biological systems, Trends Biochem. Sci, vol.24, pp.418-422, 1999.

D. Liberzon, E. D. Sontag, and Y. Wang, On integral-input-to-state stabilization, Proceedings of the American Control Conference, vol.3, pp.1598-1602, 1999.

H. Nijmeijer, . Van-der, and A. J. Schaft, Nonlinear dynamical control systems, 1990.

Z. Nitecki and M. Shub, Filtration, decompositions, explosions, American Journal of Mathematics, vol.97, pp.1029-1047, 1975.

R. Ortega, A. Loría, P. Nicklasson, and H. Sira-ramirez, Passivity-based control of euler-lagrange systems: Mechanical, electrical and elctromechanical aoolications, 1998.

I. Pchelkina and A. L. Fradkov, Control of oscillatory behavior of multispecies populations, Ecological Modelling, vol.227, pp.1-6, 2012.

A. Pisarchik and U. Feudel, Control of multistability, Physics Reports, vol.540, pp.167-218, 2014.

N. Rouche, P. Habets, and M. Laloy, Stability theory by Liapunov's direct method, 1977.

V. Rumyantsev and A. Oziraner, Stability and stabilization of motion with respect to part of variables, Moscow: Nauka, 1987.

E. D. Sontag, Further facts about input-to-state stabilization, IEEE Transactions on Automatic Control, vol.35, pp.473-476, 1990.

E. D. Sontag, Coments on integral variants of iss, Systems & Control Letters, vol.34, pp.93-100, 1998.

E. D. Sontag and Y. Wang, On characterizations of the input-to-state stability property, Systems & Control Letters, vol.24, pp.351-359, 1995.

E. D. Sontag and Y. Wang, New characterizations of the input-to-state stability, IEEE Transactions on Automatic Control, vol.41, pp.1283-1294, 1996.

G. Stan and R. Sepulchre, Analysis of interconnected oscillators by dissipativity theory, IEEE Trans. Automatic Control, vol.52, pp.256-270, 2007.

V. Vorotnikov, Partial stability and control, 1998.

V. Yakubovich, G. Leonov, and A. Gelig, Stability of stationary sets in control systems with discontinuous nonlinearities, 2004.

, Nitecki & Shub, 1975) Let ? 1 , · · · , ? k be a decomposition of ?, then

, An r-cycle (r ? 2) is an ordered r-tuple of distinct indices i 1 , · · · , i r such that ? i1 ? · · · ? ? ir ? ? i1