Semi-Global Stabilization of A Class of Underactuated Euler-Lagrange Systems by Backstepping Approach

For a class of underactuated Euler-Lagrange systems, a new approach for semi-global stabilization is presented. By defining a linear combination function of configuration variables and the momentum conjugates to the unactuated variables as an error variable and applying the standard backstepping design technique without any additional complex nonlinear transformation, the closed loop dynamics of this error variable is transformed into a second-order linear stable system. The design procedure is applied to an inverted pendulum system and simulation test is performed to show that the origin of closed-loop system has the semi-global domain of attraction, i.e. upper half-plane, with appropriate design parameters chosen