A note on pole assignment

This note gives an alternate proof of Davison's theorem [2] on pole placement and further shows that, for a controllable, observable system
\dot{x} = \hat{A}x + \hat{B}u, y = \hat{C}x
, the number of poles that can be assigned arbitrarily are equal to max (
m,p
), where
m
Rank
\hat{B}
and
p
= Rank
\hat{C}
. In some cases, more than max (
m,p
) poles can be assigned arbitrarily.