Nearest singular descriptor system having impulsive initial-conditions

This paper considers a distance problem: given a singular first order system, what is the distance to a nearest singular descriptor system that has impulsive initial conditions. The link between impulsive initial conditions and zeros at infinity is well-known. This paper provides bounds on the minimum perturbation required for a pair of matrices E and A such that the perturbed matrix pencil has one or more zeros at infinity. We provide closed form solutions for the minimum value for rank one perturbations.