Let A be a convex cone of n×n matrices. In this paper, we present a necessary and sufficient condition for A 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 A. This extends a previous paper by the authors, where a robust stability criterion for A was obtained.
Cohen, N., & Lewkowicz, I. (2000). A characterization of convex cones of matrices with constant regular inertia. Linear Algebra and Its Applications, 318(1–3), 23–33. https://doi.org/10.1016/S0024-3795(00)00126-9