Nonlinear \({\mathcal {H}}_\infty \) methods are explored as a means of designing robust controllers for multiple spacecraft in coordinated flight, subject to orbital perturbations. Formation flying dynamics are modelled with second- and third-order differential terms. The resulting nonlinear \({\mathcal {H}}_\infty \) control problem is solved through an analytical solution to the Hamilton-Jacobi inequality. It is shown that a linear combination of relative position and velocity feedback provides a solution to the nonlinear \({\mathcal {H}}_\infty \) state feedback control problem for formation flying. The robust controller is validated in simulation and shown to outperform a nonlinear controller designed on the same cost function.
