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

$H_{\infty}$ Inverse Optimal Attitude Tracking on the Special Orthogonal Group $SO(3)$