On the structure at infinity of linear square decoupled systems

The purpose of this note is to demonstrate that a square invertible linear system (
C, A, B
) is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems (
c'_{i}, A, B
) where
c'_{i}
denotes the
i
th row of
C
. Until now only the necessity of this condition has been established [1].