In this paper, we consider a simple robust adaptive stabilization problem based on an H∞ uncertainty model with a discrete unknown parameter. In the proposed problem formulation, the unknown plant is assumed to belong to one of N possible uncertainty models, where each model is described by a known, linear nominal plant with H∞ bounds on the unmodeled dynamics. We show that if each of the models can be robustly stabilized with a linear time-invariant (LTI) controller, then there exists a single adaptive (possibly nonlinear and time-varying) controller that simultaneously robustly stabilizes all the N possible uncertainty models. The adaptive controller can provide the same level of stability robustness as the LTI controllers, and introduces, at most, a bounded transient in the output. Our approach is based on a simple switching algorithm and a novel application of H∞ filtering methods.