M. W. Spong, Partial feedback linearization of underactuated mechanical systems, Proceedings of IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS'94), vol.1, pp.314-321, 1994.

M. Urabe, Nonlinear autonomous oscillations: Analytical theory, vol.34, 1967.

G. A. Leonov, Generalization of the Andronov-Vitt theorem, Regular and chaotic dynamics, vol.11, issue.2, pp.281-289, 2006.

J. Hauser and C. C. Chung, Converse Lyapunov functions for exponentially stable periodic orbits, Systems & Control Letters, vol.23, issue.1, pp.27-34, 1994.

G. A. Leonov and N. V. Kuznetsov, Time-varying linearization and the Perron effects, Int. J. of bifurcation and chaos, vol.17, issue.04, pp.1079-1107, 2007.

S. S. Pchelkin, A. S. Shiriaev, A. Robertsson, L. B. Freidovich, S. A. Kolyubin et al., On orbital stabilization for industrial manipulators: Case study in evaluating performances of modified PD+ and inverse dynamics controllers, IEEE Transactions on Control Systems Technology, vol.25, issue.1, pp.101-117, 2016.

C. F. Saetre, A. Shiriaev, and T. Anstensrud, Trajectory optimization and orbital stabilization of underactuated euler-lagrange systems with impacts, 2019 18th European Control Conf. (ECC), pp.758-763, 2019.

A. Mohammadi, M. Maggiore, and L. Consolini, Dynamic virtual holonomic constraints for stabilization of closed orbits in underactuated mechanical systems, Automatica, vol.94, pp.112-124, 2018.

A. S. Shiriaev, L. B. Freidovich, and I. R. Manchester, Can we make a robot ballerina perform a pirouette? orbital stabilization of periodic motions of underactuated mechanical systems, Annual Reviews in Control, vol.32, issue.2, pp.200-211, 2008.

A. Shiriaev, J. W. Perram, C. Canudas-de, and W. , Constructive tool for orbital stabilization of underactuated nonlinear systems: Virtual constraints approach, IEEE Trans. Automat. Contr, vol.50, issue.8, pp.1164-1176, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00395031

A. S. Shiriaev, L. B. Freidovich, and S. V. Gusev, Transverse linearization for controlled mechanical systems with several passive degrees of freedom, IEEE Trans. Automat. Contr, vol.55, issue.4, pp.893-906, 2010.

M. O. Surov, S. V. Gusev, and A. S. Shiriaev, New results on trajectory planning for underactuated mechanical systems with singularities in dynamics of a motion generator, 2018 IEEE Conf. on Decision and Control (CDC), pp.6900-6905, 2018.

V. Yakubovich, A linear-quadratic optimization problem and the frequency theorem for nonperiodic systems. i, Siberian Mathematical Journal, vol.27, issue.4, pp.614-630, 1986.

P. Hartman and C. Olech, On global asymptotic stability of solutions of differential equations, Trans. of the American Mathematical Society, vol.104, issue.1, pp.154-178, 1962.

G. Borg, A condition for the existence of orbitally stable solutions of dynamical systems, 1960.

S. V. Gusev, A. S. Shiriaev, and L. B. Freidovich, SDP-based approximation of stabilising solutions for periodic matrix Riccati differential equations, Int. J. of Control, vol.89, issue.7, pp.1396-1405, 2016.

J. Löfberg, YALMIP: A toolbox for modeling and optimization in MATLAB, Proc. of the CACSD Conf, vol.3, 2004.

R. H. Tütüncü, K. Toh, and M. J. Todd, Solving semidefinitequadratic-linear programs using SDPT3, Mathematical programming, vol.95, issue.2, pp.189-217, 2003.