Rotational stabilization of a rigid body using two torque actuators

A time varying stabilizing feedback controller is constructed for a rigid body with two control torques by employing trajectory interception approach. This approach does not rely on any specific choice of a Lyapunov function. The proposed feedback law is a composition of a standard stabilizing feedback control for a Lie bracket extension of the original system and a periodic continuation of a solution to an open loop trajectory interception problem of original system and its Lie bracket extension on an interval [0 T].