Stability and bifurcation properties of index-1 DAEs

Abstract

It is well known that an equilibrium of a semi-explicit, index-1 differential-algebraic equation under a parameter variation may encounter the singularity manifold. It is a generic property of this encounter that one eigenvalue of the linear stability mapping associated with the equilibrium will pass from one half of the complex plane to the other without passing through the imaginary axis. This is known as singularity-induced bifurcation and an equivalent result is proven in this paper. While this property is generic, it is shown how more than one eigenvalue can diverge in an analogous manner, with applications in electrical power systems.