  This work presents a fairly complete account on various topological and
metrical aspects of feedback stabilization for single-input-single-output
(SISO) continuous and discrete time linear-time-invariant (LTI) systems. In
particular, we prove that the set of stabilizing output feedback gains for a
SISO system with n states has at most $\lceil{\frac{n}{2}}\rceil$ connected
components. Furthermore, our analysis yields an algorithm for determining
intervals of stabilizing gains for general continuous and discrete LIT systems;
the proposed algorithm also computes the number of unstable roots in each
unstable interval. Along the way, we also make a number of observations on the
set of stabilizing state feedback gains for MIMO systems.
