Stability of a linear system $\dot x=Ax$ is equivalent to the fact
that all
roots of the characteristic polynomial $p(\lambda)=\det(A-\lambda I)$
have negative real parts. This property of roots is easily checkable.
(Because of this equivalence, a
polynomial $p(\lambda)=a_0\lambda^n+a_1\lambda^{n-1}+\ldots+a_n$
with this property is called * stable*.)

For real-life systems,
we often do not know the exact values of the coefficients of the
matrix $A$ and therefore, we do not know the exact coefficients $a_i$
of the characteristic polynomial $p(\lambda)$. How can we then check
whether the system is stable? It is known that if the set $S$ of possible
values of the coefficients $\vec a=(a_0,a_1,\ldots,a_n)$ is a convex
polytope, then the stability for * all* $\vec a\in S$ is equivalent
to the stability for all $\vec a$ from all * edges*
(one-dimensional faces) of the polytope $S$. In the paper under
review, a new method is described for checking whether all polynomials
from a given edge are stable.