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This work proposes a hybrid nonlinear output feedback control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of "lower-level" nonlinear output feedback controllers together with "upper-level" switching laws, based on available state estimates, that orchestrate the transitions between the constituent modes and their respective controllers. The output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters, to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. The switching logic tracks the evolution of the state estimates generated by the observers and orchestrates switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. The differences between the state and output feedback switching strategies are discussed and a chemical process example is used to demonstrate the proposed approach.