On pole assignment in linear multivariable systems using output feedback

The general problem of pole assignment in a linear, time-invariant multivariable system via output feedback is considered. It is shown that given a controllable-observable system (
C,A,B
) in which
A \in R^{n \times n}
, rank
B = m
, rank
C = r
, then for almost all (
B,C
) pairs,
\min (n,m + r-1)
poles can be assigned arbitrarily close to
\min (n, m + r-1
) specified symmetric values by using output feedback.