On the structure of maximal(A, B)-Invariant subspaces: A polynomial matrix approach

Given a controllable and observable triple (
A, B, C
) describing a linear time invariant multivariable system Σ, which gives rise to a full rank transfer function matrix
T_{o}(s)
, the structure of the maximal (
A, B
)- invariant subspace contained in
\ker C
is investigated using a polynomial matrix approach. Thus, certain connections between the geometric and the polynomial matrix approaches to linear system theory are established.