Consider the vector differential delay equation
where the matrices and admit a simultaneous triangulation. The authors introduce the surface in
which is called the stability cone. They prove the following
Theorem. Let , , , where and are lower triangular matrices with entries , , respectivey. Let the points be defined by
Equation is asymptotically stable if and only if all the points lie inside the stability cone . If there exists a point lying outside the stability cone, then is unstable.