D. M. Alonso, E. E. Paolini, and J. L. Moiola, Controlling an Inverted Pendulum with Bounded Controls, Lecture Notes in Control and Information Sciences, 2002.
DOI : 10.1007/3-540-45606-6_1

D. M. Alonso, E. E. Paolini, and J. L. Moiola, Global Bifurcation Analysis of a Controlled Underactuated Mechanical System, Nonlinear Dynamics, vol.197, issue.3?4, pp.205-225, 2005.
DOI : 10.1007/978-1-4757-2421-9

S. Andary, A. Chemori, M. Benoit, and J. Sallantin, A dual model-free control of underactuated mechanical systems, application to the inertia wheel inverted pendulum, 2012 American Control Conference (ACC), 2012.
DOI : 10.1109/ACC.2012.6315492
URL : https://hal.archives-ouvertes.fr/lirmm-00723934

S. Andary, A. Chemori, and S. Krut, Control of the underactuated inertia wheel inverted pendulum 290 for stable limit cycle generation, RSJ Advanced Robotics, vol.23, 1999.

S. Andary, A. Chemori, and S. Krut, Estimation-based disturbance rejection in control for limit cycle generation on inertia wheel inverted pendulum testbed, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.1302-1307, 2009.
DOI : 10.1109/IROS.2009.5354120
URL : https://hal.archives-ouvertes.fr/lirmm-00429808

A. Dhooge, W. Govaerts, and Y. A. Kuznetsov, MATCONT, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.141-164, 2003.
DOI : 10.1145/779359.779362

A. Fradkov and A. Pogromsky, Introduction to control of oscillations and chaos, 1998.
DOI : 10.1142/3412

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

N. Khraief-haddad, A. Chemori, and S. Belghith, External disturbance rejection in ida-pbc controller for underactuated mechanical systems: From theory to real-time experiments, p.14, 2014.
URL : https://hal.archives-ouvertes.fr/lirmm-01722715

N. Khraief-haddad, A. Chemori, J. J. Pena, and . Belghith, Stabilization of inertia wheel inverted pendulum by model reference adaptive ida-pbc : From simulation to real-time experiments, 3rd International Conference on Control, Engineering and Information Technology -CEIT'15, 2015.

C. Kuehn, FROM FIRST LYAPUNOV COEFFICIENTS TO MAXIMAL CANARDS, International Journal of Bifurcation and Chaos, vol.7, issue.05, pp.1467-1475, 2010.
DOI : 10.1007/978-1-4613-0003-8

N. Leonard, A. Bloch, and J. Marsden, Mechanical Feedback Control Systems, Open Problems in Mathe-matical Systems and Control Theory, 1998.

J. Marsden and M. Mccracken, The Hopf Bifurcation and Its Applications, 1976.
DOI : 10.1115/1.3424264

S. Nikolov and V. Nedev, Abstract, Journal of Theoretical and Applied Mechanics, vol.46, issue.1, pp.17-32, 2016.
DOI : 10.1515/jtam-2016-0002

R. Ortega, M. Spong, F. Gomez-estern, and G. Blankenstein, Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment, IEEE Transactions on Automatic Control, vol.47, issue.8, 2002.
DOI : 10.1109/TAC.2002.800770

D. Pagano, L. Pizarro, and J. Aracil, LOCAL BIFURCATION ANALYSIS IN THE FURUTA PENDULUM VIA NORMAL FORMS, International Journal of Bifurcation and Chaos, vol.10, issue.05, pp.981-995, 2000.
DOI : 10.1243/PIME_PROC_1992_206_043_02

A. F. Palacios, The Hamilton-Type Principle in Fluid Dynamics, 2006.

V. Santibañez, R. Kelly, and J. Sandoval, Control of the inertia wheel pendulum by bounded 325 torques, Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC'05. 44th IEEE Conference on (IEEE), pp.8266-8270, 2005.

S. Wiggins, Introduction to Applied Nonlinear Dynamical systems and Chaos, 2003.