Rotational stabilization of a rigid body using two torque actuators

The Hamilton-Jacobi-Bellman theorem is used to derive a control law that globally asymptotically stabilizes Euler´s equation to a prescribed state. It is shown that if all three components of the prescribed state are nonzero, then it is impossible to asymptotically stabilize Euler´s equation to that state using only two torque inputs along two principal axes. If two components of the prescribed state are nonzero and one of the two components is in the uncontrolled principal axes, then a family of optimal nonlinear stabilizing feedback control laws is obtained