  In this paper, we consider the problem of computing the nearest
uncontrollable (C-uncontrollable) system to a given higher order system. The
distance to the nearest uncontrollable system, also termed as the radius of
controllability, is a good measure of gauging the numerical robustness of the
given system with respect to controllability. Here, we invoke the equivalence
of C-controllability of a higher order system with full rank property of a
certain Toeplitz structured matrix. This enables us to pose the problem of
computing the radius of controllability as equivalent to the problem of
computing the nearest structured low rank approximation of this Toeplitz
structured matrix. Through several numerical examples and comparison with the
benchmark numerical problem, we illustrate that our approach works well.
