Global null controllability of perturbed linear periodic systems

In this note we study the global null controllability with bounded controls of perturbed linear periodic systems in R
ⁿ
. More explicitly, a globally null controllable periodic system is perturbed by suitably small terms
V(t)
and
C(t)
to obtain a system of the form
\dot{x} = (A(t) + V(t))x + (B(t) + C(t))u
and sufficient conditions are given to ensure the global null controllability of the resulting perturbed system.