Instabilities in the feedback linearization of a double inverted pendulum

Numerical results in the feedback linearization of a double pendulum system are presented. Singularities in the vector field of the closed-loop system manifest themselves as numerical instabilities when the denominator of the linearizing control input is sufficiently small. In a practical example, such as balancing a two-link manipulator along an equilibrium manifold, a method to steer the system away from an ill-conditioned control law is suggested.<>