D. Angeli, An Almost Global Notion of Input-to-State Stability, IEEE Transactions on Automatic Control, vol.49, issue.6, pp.866-874, 2004.
DOI : 10.1109/TAC.2004.829594

D. Angeli and D. Efimov, On Input-to-State Stability with respect to decomposable invariant sets, 52nd IEEE Conference on Decision and Control, 2013.
DOI : 10.1109/CDC.2013.6760819

D. Angeli and D. Efimov, Characterizations of Input-to-State Stability for Systems With Multiple Invariant Sets, IEEE Transactions on Automatic Control, vol.60, issue.12, pp.3242-3256, 2015.
DOI : 10.1109/TAC.2015.2418676

URL : https://hal.archives-ouvertes.fr/hal-01136819

D. Angeli, J. E. Ferrell, and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proc. Natl. Acad. Sci. USA, pp.1822-1827, 2004.
DOI : 10.1073/pnas.0308265100

D. Angeli and L. Praly, Stability Robustness in the Presence of Exponentially Unstable Isolated Equilibria, IEEE Transactions on Automatic Control, vol.56, issue.7, pp.1582-1592, 2011.
DOI : 10.1109/TAC.2010.2091170

URL : https://hal.archives-ouvertes.fr/hal-00554432

D. Angeli and E. D. Sontag, Multi-stability in monotone input/output systems, Systems & Control Letters, vol.51, issue.3-4, pp.185-202, 2004.
DOI : 10.1016/j.sysconle.2003.08.003

N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, 1970.
DOI : 10.1007/978-3-642-62006-5

M. Chaves, T. Eissing, and F. Allgower, Bistable Biological Systems: A Characterization Through Local Compact Input-to-State Stability, IEEE Transactions on Automatic Control, vol.53, issue.Special Issue, pp.87-100, 2008.
DOI : 10.1109/TAC.2007.911328

F. Dörfler and F. Bullo, Breaking the Hierarchy: Distributed Control and Economic Optimality in Microgrids, IEEE Transactions on Control of Network Systems, vol.3, issue.3, 2014.
DOI : 10.1109/TCNS.2015.2459391

D. Efimov, Global Lyapunov Analysis of Multistable Nonlinear Systems, SIAM Journal on Control and Optimization, vol.50, issue.5, pp.3132-3154, 2012.
DOI : 10.1137/090767509

URL : https://hal.archives-ouvertes.fr/hal-00745623

D. Efimov, R. Ortega, and J. Schiffer, ISS of multistable systems with delays: Application to droop-controlled inverter-based microgrids, 2015 American Control Conference (ACC), pp.2341-2346, 2015.
DOI : 10.1109/ACC.2015.7172064

URL : https://hal.archives-ouvertes.fr/hal-01140346

D. Efimov, W. Perruquetti, and M. Petreczky, On necessary conditions of instability and design of destabilizing controls, 53rd IEEE Conference on Decision and Control
DOI : 10.1109/CDC.2014.7039997

URL : https://hal.archives-ouvertes.fr/hal-01066282

D. Efimov, J. Schiffer, and R. Ortega, Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids, International Journal of Control, vol.99, issue.5, pp.909-918, 2016.
DOI : 10.1109/JPROC.2010.2080250

URL : https://hal.archives-ouvertes.fr/hal-01211454

D. V. Efimov and A. L. Fradkov, Oscillatority of Nonlinear Systems with Static Feedback, SIAM Journal on Control and Optimization, vol.48, issue.2, pp.618-640, 2009.
DOI : 10.1137/070706963

F. Forni and R. Sepulchre, Differential analysis of nonlinear systems: Revisiting the pendulum example, 53rd IEEE Conference on Decision and Control, pp.3848-3859, 2014.
DOI : 10.1109/CDC.2014.7039987

A. Kh, G. A. Gelig, V. A. Leonov, and . Yakubovich, Stability of nonlinear systems with non unique equilibrium, 1978.

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

H. K. Khalil, Nonlinear Systems, 1992.

V. Lakshmikantham and X. Z. Liu, Stability analysis in terms of two measures, World Scientific, 1993.
DOI : 10.1142/2018

G. A. Leonov, On the boundedness of the trajectories of phase systems, Siberian Mathematical Journal, vol.8, issue.No. 6, pp.491-495, 1974.
DOI : 10.1007/BF00969820

Y. Lin, E. D. Sontag, and Y. Wang, A Smooth Converse Lyapunov Theorem for Robust Stability, SIAM Journal on Control and Optimization, vol.34, issue.1, pp.124-160, 1996.
DOI : 10.1137/S0363012993259981

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

Z. Nitecki and M. Shub, Filtrations, Decompositions, and Explosions, American Journal of Mathematics, vol.97, issue.4, pp.1029-1047, 1975.
DOI : 10.2307/2373686

E. J. Noldus, New direct lyapunov-type method for studying synchronization problems, Automatica, vol.13, issue.2, pp.139-151, 1977.
DOI : 10.1016/0005-1098(77)90038-3

R. Ortega, M. Galaz, A. Astolfi, Y. Sun, and T. Shen, Transient stabilization of multimachine power systems with nontrivial transfer conductances, IEEE Transactions on Automatic Control, vol.50, issue.1, pp.60-75, 2005.
DOI : 10.1109/TAC.2004.840477

A. Rantzer, A dual to Lyapunov's stability theorem, Systems & Control Letters, vol.42, issue.3, pp.161-168, 2001.
DOI : 10.1016/S0167-6911(00)00087-6

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

J. Schiffer and F. Dörfler, On stability of a distributed averaging PI frequency and active power controlled differential-algebraic power system model, 2016 European Control Conference (ECC), pp.1487-1492, 2016.
DOI : 10.1109/ECC.2016.7810500

J. Schiffer, R. Ortega, A. Astolfi, J. Raisch, and T. Sezi, Conditions for stability of droop-controlled inverter-based microgrids, Automatica, vol.50, issue.10, pp.502457-2469, 2015.
DOI : 10.1016/j.automatica.2014.08.009

URL : https://hal.archives-ouvertes.fr/hal-01262877

E. D. Sontag and Y. Wang, On Characterizations of Input-to-State Stability with Respect to Compact Sets, Proc IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), pp.226-231, 1995.
DOI : 10.1016/B978-0-08-042371-5.50039-3

E. D. Sontag, On the Input-to-State Stability Property, European Journal of Control, vol.1, issue.1, pp.24-36, 1995.
DOI : 10.1016/S0947-3580(95)70005-X

E. D. Sontag and Y. Wang, New characterizations of input-to-state stability, IEEE Transactions on Automatic Control, vol.41, issue.9, pp.1283-1294, 1996.
DOI : 10.1109/9.536498

G. Stan and R. Sepulchre, Analysis of Interconnected Oscillators by Dissipativity Theory, IEEE Transactions on Automatic Control, vol.52, issue.2, pp.256-270, 2007.
DOI : 10.1109/TAC.2006.890471

Y. Tang, F. Qian, H. Gao, and J. Kurths, Synchronization in complex networks and its application ??? A survey of recent advances and challenges, Annual Reviews in Control, vol.38, issue.2, pp.184-198, 2014.
DOI : 10.1016/j.arcontrol.2014.09.003

S. Trip, C. D. Bürger, and . Persis, An internal model approach to frequency regulation in inverter-based microgrids with time-varying voltages, 53rd IEEE Conference on Decision and Control, pp.223-228, 2014.
DOI : 10.1109/CDC.2014.7039385

S. Trip, M. Bürger, and C. D. Persis, An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages, Automatica, vol.64, pp.240-253, 2016.
DOI : 10.1016/j.automatica.2015.11.021

P. Varaiya, F. F. Wu, and R. Chen, Direct methods for transient stability analysis of power systems: Recent results, Proceedings of the IEEE, pp.1703-1715, 1985.
DOI : 10.1109/PROC.1985.13366

J. F. Vasconcelos, A. Rantzer, C. Silvestre, and P. J. Oliveira, Combination of Lyapunov and Density Functions for Stability of Rotational Motion, IEEE Transactions on Automatic Control, vol.56, issue.11, pp.562599-2607, 2011.
DOI : 10.1109/TAC.2011.2123290

V. A. Yakubovich, G. A. Leonov, A. Kh, and . Gelig, Stability of stationary sets in control systems with discontinuous nonlinearities, of Series on stability, vibration, and control of systems, 2004.
DOI : 10.1142/5442