Pole assignment in linear multivariable systems using observers of reduced order

In linear multivariable systems it is of interest to achieve pole assignment using observers of reduced order. In this correspondence it is shown that for almost all systems with
r
independent inputs and
m
independent outputs, pole assignment can be obtained using an observer the order of which is
\max(0,n + 1-m-r)
or
\lceil(n+1-r)/m\rceil-1
, where
n
is the dimension of the state space and
\lceil a \rceil
denotes the least integer greater than or equal to number
a
. The related procedures for desioning the controllers are given.