This paper presents and compares two approaches for the torque converter clutch slip control when the friction coefficient of the clutch has uncertainty. The main objective of the clutch slip control is to improve the fuel efficiency of a vehicle with an automatic transmission. One important issue of the clutch slip control is to maintain good performance when the clutch friction coefficient changes as the slip speed changes. This problem becomes a challenge if the friction coefficient decreases significantly as the slip speed increases, since the system may become unstable under this circumstance. In this paper the rate of the friction coefficient change to the slip speed change is considered as the variable of robustness to test the designed controllers.