Robustness of backstepping adaptive control with respect to inverse multiplicative uncertainty

We deal with robustness of the tuning function backstepping adaptive control with respect to inverse multiplicative unmodeled dynamics and external disturbances. Under assumptions comparable to those used in the certainty equivalence schemes, it is shown that the closed loop is locally stable with a region of attraction inversely proportional to the "size" of the unmodeled dynamics. Furthermore, the tracking error is shown to be proportional to the "size" of the external disturbances