This study compares four control laws for stationkeeping around Phobos. The dynamics of the Mars-Phobos system are constrained to the synodical plane of the circular restricted three-body problem (CRTBP) with Phobos modelled as an ellipsoid. A novel method of determining the necessary conditions for periodic orbits is formulated through nonlinear optimization techniques. The optimization algorithm is a Nelder-Mead simplex and is shown to outperform any gradient-based methods as well as other techniques for determining such orbits. Two controllers, constant feedback and scheduled, are developed from the algebraic Riccati equation. These controllers are then compared to the optimal solution which uses the time-varying Riccati equation. A fourth controller is developed based on a Floquet-Lyapunov transformation of the system. At high orbits, the periodicity of the linearized system is very small and the optimal controllers perform equally well. As periodicity increases with closer orbits, time-varying feedback becomes necessary for increased controller performance.