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 sysytem and approximate linear system appears as a change of the relative degree structure. By comparison of these two structure, the necessary condition for the input-output linearization method to have no singular point at the equilibrium is derived. Based on this fact, the selection of the output function is proposed. Moreover the output design method for linear stable zero dynamics is proposed.
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