In this paper, the author considers
controlled objects (called * plants* in control theory)
that can be described by differential equations of the following type:
$${d^nx\over dt^n}+b_{n-1}{d^{n-1}x\over dt^{n-1}}+...+b_0=
{d^mu\over dt^m}+a_{m-1}{d^{m-1}u\over dt^{m-1}}+...+a_0,$$
where $x(t)$ is the state
of the plant at the moment $t$, and $u(t)$ is the value of the control
applied at the moment $t$. The plant is called * proper* if $m\le
n$. A plant is called * stabilizable* if there exists a *
controller*, i.e., another
differential equation that describe $u$ in terms of $x$ so that
the system of these two equations is * stable* (crudely speaking,
small deviations from the initial conditions tend to 0 as
$t\to\infty$). A plant is called * strongly stabilizable* if it can
be stabilized by a proper controller that is not only stable with the
plant attached, but also stable by itself. There exists a simple
method for checking whether a given plant is strongly stabilizable.

In real life, we often only know the {\it intervals} $[a^-_i,a^+_i]$ and $[b^-_j,b^+_j]$ of possible values of $a_i$ and $b_j$. Given these intervals, we want to check whether we can conclude that the actual plant (with some unknown values $a_i\in [a^-_i,a^+_i]$ and $b_j\in [b^-_j,b^+_j]$) is strongly stabilizable, or there are some values $a_i$ and $b_j$ from the given intervals for which the plant is not strongly stabilizable.

One necessary condition for strong stabilizability is known: that the polynomials $a(s)=s^m+\sum a_i s^i$ and $b(s)=s^n+\sum b_js^j$ (where $s=i\omega$ is related to the parameter $\omega$ of the Fourier transform) have no common complex roots in the unstable zone ${\rm Re} (s)\ge 0$.

The author shows that under this condition, all plants from a given interval plant are strongly stabilizable iff the following two of them are: we take any vector $b_0\in [b^-_0,b^+_0], \ldots,b_{n-1}\in [b^-_{n-1},b^+_{n-1}]$, and take $a_i=a^-_i$ ($0\le i\le m-1$) for the first plant and $a_i=a^+_i$ ($0\le i\le m-1$) for the second plant.

Thus, to check strong stabilizability of an interval plant $I$, it suffices to check two vertices of the box that describes all possible plants from $I$.