Quasihomogeneity Approach to the Pendubot Stabilization around Periodic Orbits

Bartolini, 2000, Chattering avoidance by second-order sliding mode control, IEEE Trans. Autom. Contr, AC-43, 241 Bhat, 1997, Finite-Time Stability of Homogeneous Systems, 2513 Berkemeier, 1999, Tracking Fast Inverted Trajectories of the Underactuated Acrobot, IEEE Trans. Robotics and Aut, 15, 740, 10.1109/70.782028 Canudas-de-Wit, 2002, Orbital Stabilization of Under-actuated Mechanical Systems Chevallereau, 2003, Rabbit: A testbed for advance control theory, IEEE Control Systems Magazine, 57, 10.1109/MCS.2003.1234651 Fantoni, 2000, Energy Based Control of the Pendubot, IEEE Trans. Aut. Contr, 45, 725, 10.1109/9.847110 Fridman, 1996, Higher order sliding modes as a natural phenomenon in control theory, in Robust Control via variable structure and Lyapunov techniques, 217, 107 Fridman, 2002, Higher order sliding modes, 53 Hong, 2001, On an output feedback finite-time stabilization problem, IEEE Trans. Auto. Ctrl, 46, 305, 10.1109/9.905699 Khalil, 2002 Levant, 1993, Sliding order and sliding accuracy in sliding mode control, Int. J. Contr, 58, 1247, 10.1080/00207179308923053 Orlov, 2003, Finite time stability of homogeneous switched systems, 4271 Orlov, 2003, Switched chattering control vs. backlash/friction phenomena in electrical servo-motors, Int. J. Contr, 76, 959, 10.1080/0020717031000099056 Orlov, 2003, Global position regulation of friction manipulators via switched chattering control, Int. J. Contr, 76, 1446, 10.1080/0020717031000149627 Rosier, 1992, Homogeneous Lyapunov function for homogeneous conitnuous vector field, Syst. Contr. Lett, 19, 467, 10.1016/0167-6911(92)90078-7 Spong, 1995, The Swing Up Contol Problem for the Acrobot’, IEEE Control Systems Magazine, 49, 10.1109/37.341864 Spong, 1997, Control of Underactuated Mechanical Systems Using Switching and Saturation, 163, 10.1007/BFb0036093 Zhang, 2002, Hybrid control of the Pendubot, IEEE Trans. Mechatronics, 7, 79, 10.1109/3516.990890 Utkin, 1999 Wang, 2000, Extremun Seeking for Limit Cycle Minimization, IEEE Trans. Aut. Contrl, 45, 2432, 10.1109/9.895589