A characterization of convex cones of matrices with constant regular inertia Original Research Article

Let image be a convex cone of n×n matrices. In this paper, we present a necessary and sufficient condition for image to contain matrices with a constant regular inertia, based on a version of the Lyapunov equation. The condition involves only the normalized extreme points of image. This extends a previous paper by the authors, where a robust stability criterion for image was obtained.