Let $(A,B)$ be a pair of matrices representing a time-invariant linear
system $\dot x(t)=Ax(t)+Bu(t)$ under block-similarity equivalence.
In this paper we measure the distance between a controllable pair of
matrices $(A,B)$ and the nearest uncontrollable one.
A bound is obtained in terms of singular values of the controllability
matrix $C(A,B)$ associated to the pair. This bound is not simply based
on the smallest singular value of $C(A,B)$ contrary to what one may
Also a lower bound is obtained using geometrical techniques expressed
in terms of the singular values of a matrix representing the tangent
space of the orbit of the pair $(A,B)$.