This research proposes to develop an innovative methodology for estimating the stability regions of large-scale nonlinear dynamical systems. The significance of the proposed methodology include: (1) its computational efficiency, (2) its ability to significantly reduce the conservativeness in estimating the stability regions, (3) its adaptability (this methodology is very general; it can stand by itself or it can be synthesized with existing methods in the way that they serve the input of the proposed methodology) and (4) its sound theoretical basis. At present, there does not exist any method that is computationally practical, yet does not yield undesirably conservative result in estimating the stability regions for large- scale nonlinear dynamical systems. The existence of such a practical method is very important for many engineering and scientific applications, as well as for many emerging research areas. The proposed research is to meet this pressing need. Also, the proposed methodology opens new areas for research, both in the area of methodology development and in the area of new applications.
