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Input output linearization of nonlinear systems by output feedback

We give necessary and sufficient conditions for static output feedback I/O linearizability of non-affine systems. We then show how to remove one of the latter conditions to form a set of sufficient conditions for the dynamic output feedback I/O linearization problem. Moreover we show that under these sufficient conditions it is always possible to design a dynamic output feedback which not only linearizes the I/O response, but also preserves the zero dynamics of the system.