1. A method of analyzing the stability of a networked power system, comprising: storing a reduced state model of the power system in memory of a computer and integrating over the model to derive a fault-on trajectory; storing in memory of the computer a numerical energy function for a post-fault condition of the power system; using the computer to compute the exit point at which a projected fault-on trajectory reaches a first local maximum of potential energy; using the exit point as an initial point and then using the computer to solve the post-fault reduced-state system; using the computer to determine the controlling unstable equilibrium point (CUEP) with respect to the fault-on trajectory of the original system by applying a homotopy algorithm that uses the exit point as the initial condition; computing a numerical energy function at the CUEP to determine a critical energy value; calculating the value of numerical energy function at a time of fault clearance using an initial condition of the post-fault trajectory; and using the computer to test if the value of the numerical energy function is less than the critical energy value: (a) if so, reporting that the initial condition lies within the stability boundary; and (b) if not, reporting that the initial condition may be unstable.