  The problem of attitude tracking using rotation matrices is addressed using
an approach which combines inverse optimality and $\mathcal{L}_{2}$ disturbance
attenuation. Conditions are provided which solve the inverse optimal nonlinear
$H_{\infty}$ control problem by minimizing a meaningful cost function. The
approach guarantees that the energy gain from an exogenous disturbance to a
specified error signal respects a given upper bound. For numerical simulations,
a simple problem setup from literature is considered and results demonstrate
competitive performance.
