This paper proposes a stability analysis method based on the higher order derivatives of ULNs. In the proposed method, the following are proposed. Firstly, if the absolute values of the first order derivatives of any coordinates of the original trajectory with respect to any initial disturbances approach zero at time infinity, then the trajectory is locally asymptotically stable. Secondly, the locally asymptotically stable region, where asymptotical stability is secured approximately, is obtained by neglecting the higher order derivatives until nth order with epsilon approximation.