A globally stable linear attitude regulator

The problem considered in this paper is that of designing an attitude regulator for an arbitrary rigid body. The design criterion is that, in the presence of no disturbance torques on the body, the system should have only one equilibrium point, and this point should be asymptotically stable for arbitrary initial conditions. By use of Lyapunov techniques and an appropriate choice of state variables, it is shown that this criterion can be satisfied by employing a linear feedback law with constant coefficients.