Using the calculated \( H_\infty \) limited controllers in the attached plot I show that as \( \gamma \) decreases the phase margin and the gain margin both increase. It also shows that the gain and phase margin are strongly correlated. In the plot the gamma is represented by the colors in the color bar and the current LIGO controller is shown as a blue triangle. The different lines of points are diffrent F1 gains and show that the relation between the gain margin and the phase margin is not always linear. However, generally speaking, this shows that gain margin and phase margin can be used somewhat interchangeably in this case. I'm not sure if this extends to all admissible controllers.