The problem of robustly, asymptotically stabilizing a point (or a set) with two output-feedback hybrid controllers is considered. These control laws may have different objectives, e.g., the closed-loop systems resulting with each controller may have different attractors. We provide a control algorithm that combines the two hybrid controllers to accomplish the stabilization task. The algorithm consists of a hybrid supervisor that, based on the values of plant's outputs and (norm) state estimates, selects the hybrid controller that should be applied to the plant. The accomplishment of the stabilization task relies on an output-to-state stability property induced by the controllers, which enables the construction of an estimator for the norm of the plant's state. The algorithm is motivated by and applied to robust, semiglobal stabilization problems uniting two controllers. (C) 2013 Elsevier Ltd. All rights reserved.