In this paper, we show that the hybrid controller that is induced by a Synergistic Lyapunov Function and Feedback (SLFF) pair relative to a compact set, can be extended to the case where the original affine control system is subject to a class of additive disturbances known as matched uncertainties, provided that the estimator dynamics do not add new equilibria to the closed-loop system. We also show that the proposed adaptive hybrid controller is amenable to backstepping. Finally, we apply the proposed hybrid control strategy to the problem of global asymptotic stabilization of a compact set in the presence of an obstacle and we illustrate this application by means of simulation results.