On the structure at infinity of linear block-decouplable systems: The general case

The aim of this note is to show that a linear system (
C, A, B
) is block-decouplable by means of static state feedback laws (
F, G
) with
G
invertible if and only if the infinite structure of (
C, A, B
) equals the union of the infinite structures of the subsystems (
C_{i}, A, B
) extracted from the given output partition. This result generalizes the ones recently obtained for Morgan's problem [6] and for the particular cases of right-invertible [7] or left-invertibie [8] systems.