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.