My research interests center on nonlinear stability and control theory, with particular emphasis on applications in electric power systems.My work in this area has focused on a number of topics. The first was the problem of identifying region-of-attraction estimates in systems described by ordinary differential equations with algebraic constraints, sometimes referred to as "semi-implicit" systems, but only recently have received attention in the literature on direct methods of transient stability analysis.Region-of-attraction estimates have important practical application in determining the ability of a power system to recover from line faults, load disturbances , and loss of generation. A second area of research in electric power systems involves illuminating the relationship between stability properties of deterministic models for the power system and exit-time statistics in a stochastic differential equation model having broad-band random disturbances in the load term. Using results from optimal control theory, we have demonstrated a closed form expression for the so-called "quasi potential" function for the power system, and shown its relationship to a standard deterministic Lyapunov function.This result offers considerable promise in yielding practically implementable algorithms to indicate in real time the vulnerability of the power system to such phenomena as voltage collapse. A third area of my research that ties developments in modern control theory with power systems applications, is the topic of "robust stability."A power system is a highly nonlinear system, whose operating point is continually changing in time.We are extending results in robust control theory to obtain a means of guaranteeing stable operation of the system over a whole range of operating points, and examining the development of algorithms for application to large scale systems.