  The notion of feedback integrators permits Euclidean integration schemes for
dynamical systems evolving on manifolds. Here, a constructive Lyapunov function
for the attitude dynamics embedded in an ambient Euclidean space has been
proposed. We then combine the notion of feedback integrators with the proposed
Lyapunov function to obtain a feedback law for the attitude control system. The
combination of the two techniques yields a domain of attraction for the closed
loop dynamics, where earlier contributions were based on linearization ideas.
Further, the analysis and synthesis of the feedback scheme is carried out
entirely in Euclidean space. The proposed scheme is also shown to be robust to
numerical errors.
