On the basis of the controlled Lagrangians, a stabilization controller is designed for the two degrees of
freedom (2-DOF) Pendubot in the vertical plane. Because the actuated variable of the system is a cyclic variable of its
original kinetic energy, the kinetic energy equation in the matching condition degenerates into an ordinary differential
equation with the controlled kinetic energy maintaining the identical cyclic variable. Taking this degeneration, a
nonlinear smooth state feedback control law is obtained, which can achieve local asymptotic stabilization for a class of
the 2-DOF Pendubots.