AbstractLiapunov's direct method is used to obtain regions of asymptotic stability for nonlinear systems with natural boundaries. In some cases this leads to larger stable regions of interest than if the bounds had been neglected. With account taken of the natural boundaries, a design method is formulated to find controller gains that give stable responses for anticipated disturbances. To compare the stability effects of different controllers and their gains, the change in the shape of the Liapunov function must be considered as well as the change in size of the region in which its time derivative is negative definite. Neglect of changes in the shape of the Liapunov function has led to misleading conclusions in previous work.