A stability theory of differential-algebraic systems such as the power system

Develops a mathematically precise and physically meaningful theory base for system stability for a general large nonlinear power system. The results are general in the sense that no specific form of parameter dependent differential-algebraic equations is assumed. Viewing the singular set as an impasse surface need not be a realistic interpretation for every differential-algebraic system. For differential-algebraic equations with a physically valid fast dynamics, trajectories may exhibit jumps or discontinuities near the singularity which can actually be calculated. In this case the regions of attractions as defined and analyzed provide conservative, and, possibly, the only reasonable estimates for the full regions of stability