In order to check that a given control $u=Kx$ makes a given system
$\dot x={\bf A}x+{\bf B}u$ with intervally uncertain coefficient
matrices $\bf A$ and $\bf B$ stable, we must check whether
the interval matrix ${\bf A}+{\bf B}K$ is * stable* (i.e., whether
${\rm Re}(\lambda)<0$ for all its eigenvalues $\lambda$).
In general, checking
stability is an NP-hard problem. There exist several algorithms for
checking stability (including several proposed by J. Rohn); these
algorithms require, in the worst case, exponentially long time.

In this paper, the author proposes several new, easily checkable, sufficient criteria for stability of interval matrices.