Power systems are extremely non-linear systems which require substantial modeling and control efforts to run continuously. The movement of the power system in parameter and state space is often not well understood, thus making it difficult or impossible to determine whether the system is nearing instability. This dissertation demonstrates several ways in which the power system stability boundary can be calculated. The power system movements evaluated here address the effects of inter-area oscillations on the system which occur in the seconds to minutes time period. The first uses gain scheduling techniques through creation of a set of linear parameter varying (LPV) systems for many operating points of the non-linear system. In the case presented, load and line reactance are used as parameters. The scheduling variables are the power flows in tie lines of the system due to the useful information they provide about the power system state in addition to being available for measurement. A linear controller is developed for the LPV model using H₂/H∞ with pole placement objectives. When the control is applied to the non-linear system, the proposed algorithm predicts the response of the non-linear system to the control by determining if the current system state is located within the domain of attraction of the equilibrium. If the stability domain contains a convex combination of the two points, the control will aid the system in moving towards the equilibrium. The second contribution of this thesis is through the development and implementation of a pseudo non-linear evaluation of a power system as it moves through state space. A system linearization occurs first to compute a multi-objective state space controller. For each contingency definition, many variations of the power system example are created and assigned to the particular contingency class. The powerflow variations and contingency controls are combined to run sets of time series analysis in which the Lyapunov function is tracked over three time steps. This data is utilized for a classification analysis which identifies and classifies the data by the contingency type. The goal is that whenever a new event occurs on the system, real time data can be fed into the trained tree to provide a control for application to increase system damping. / Ph. D.