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. A gap between an original nonlinear system and an approximate linear system appears as a change of the relative degree structure. The gap is overcome by designing special functios. Using these functions, a neccessary and sufficient condition is proposed that a function has invariant relative degree over a state space.
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