Nth order asymptotic orbital stability analysis method has been proposed to determine whether a nonlinear system is stable or not with large fluctuations of the system states. In this paper, we discuss the stability of robust control of a nonlinear crane system using this method. The robust control system studied is more stable than ordinary control system even with the large disturbances. Nth order asymptotic orbital stability analysis is described by using the higher order derivatives of universal learning networks (ULNs), and ULNs are tools for modeling, managing and controlling large scale complicated systems such as economic, social and living systems as well as industrial plants. In this paper, robust control system is constructed by ULNs too, and the controller is best tuned through learning. Finally, simulations of 1st order orbital change of a nonlinear crane system are carried out. From results of simulations, it is shown that the robust control method have better performance and robustness than commonly used method.