We study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties. Our approach relies on well-known H-infinity linear control tools and allows one to recover and improve, in the unifying framework of a semiglobal separation result, existing results on the semiglobal stabilization via output feedback. In particular, we discuss the case of uncorrupted outputs, input and output nonlinearities, or model uncertainties, which may include, for example, practical situations such as backlash, hysteresis, and saturations. The key feature of our design procedure is given by the choice of two continuous functions: the first one is instrumental in constructing a stabilizing controller; the second one arises in the candidate Lyapunov function for the closed-loop system. Relying on our main theorem, we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems.