Stabilization of Spacecraft Flight in Halo Orbits: An$H_infty $Approach

The problem of stabilizing the motion of a spacecraft in an unstable orbit around the interior Sun–Earth libration point (
$L_1$
) is addressed in this paper. Modern control techniques, which extend the traditional
$ cal H_infty $
framework to periodic discrete linear time-varying systems, are employed in the solution of the problem. Nonlinear simulation results are presented and it is shown that the control effort required can be provided by next-generation electric propulsion systems.