A linear system $\dot x=Ax$ is stable iff its characteristic polynomial $p(z)=\det(A-zI)$ is stable, i.e., if all its roots have negative real parts.

For polynomials with interval coefficients, Kharitonov has proposed a
criterion for stability: namely, to check that * all* polynomials
from an interval family are stable, it is sufficient to check that 4
special polynomials from this family are stable.

The authors show that for polynomials of order $n$, this checking requires $O(n^2)$ computational steps.