V. Blondel, "On interval polynomials with no zeros in the unit disc", IEEE Transactions on Automatic Control, 1995, Vol. 40, No. 3, pp. 479-480.

It is well known that a discrete-time linear system $x(k+1)=Ax(k)$ if stable iff the eigenvectors $\bar x$ of $A$ (i.e., vectors for which $A\bar x=\lambda\bar x$ for some $\lambda$) lead to stable trajectories $x(k)=\lambda^k\bar x$, i.e., iff $\lambda^k\to 0$ when $k\to\infty$. This, in its turn, is equivalent to $|\lambda|<1$. One way to compute eigenvalues of a given matrix $A$ is to take into consideration that eignevalues are roots of the the characteristic polynomial $\bar p(\lambda)=\det(A-\lambda I)$. In terms of $p$, the above condition means that all roots of the polynomial $\bar p(\lambda)=p_0\lambda^n+p_1\lambda^{n-1}+...+p_n$ must be inside the open unit disk. It is often convenient to consider a new variable $z=1/\lambda$. To guarantee stability, this new variable must satisfy the property $|z|>1$. This new variable is a root of the polynomial equation $p(z)=0$, where $p(z)=\bar p(1/\lambda)\cdot \lambda^n=p_0+p_1z+...+p_nz^n$. For this new polynomial, the stability condition is that $p(z)$ should have no zeros in the closed unit disk.

When we start with a system with interval uncertainty (i.e., with an interval matrix ${\bf A}$), we end up with a polynomial ${\bf p}(z)={\bf p}_0+{\bf p}_1 z+...+{\bf p}_nz^n$ with interval coefficients ${\bf p}_i$.

In the paper under review, a new necessary condition is formulated for all roots of an interval polynomial to be outside the closed unti disk. This condition uses only two coefficients ${\bf p}_0$ and ${\bf p}_1$.