Stability analysis of nonlinear systems using high order derivatives of universal learning networks

In this paper, a stability analysis method based on the higher order derivatives of ULNs is proposed. In the proposed method, the following are proposed. Firstly, if the absolute values of the first order derivatives of any nodes 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 comparing the first order derivatives and higher order derivatives.