Partial stabilization of underactuated Euler–Lagrange systems via a class of feedback transformations

A new class of non-trivial feedback transformations, which can be applied to any underactuated Lagrangian system, is proposed. As shown, these transformations play an important role in solving a stabilization problem with respect to a part of the actuated variables, while the given additional constraints are imposed on the rest of the variables. Theoretical results are illustrated by solving the problem of swinging up the Pendubot.