In this paper, the change of the relative degree structure at the controllable equilibrium is discussed. In the neighborhood of the controllable equilibrium, all nonlinear systems are approximated to linear controllable system. The gap between the original nonlinear system and approximate linear system appears as a change of the relative degree structure. By comparison of these two structures, the necessary and sufficient condition is derived in order for the equilibrium not to be singular point via the input-output linearization. Based on this result, the selection of the output function is proposed. Moreover the output design method for linear stable zero dynamics is proposed.
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