Decoupling by restricted static-state feedback: The general case

In this paper we tackle the general block decoupling problem, for linear constant dynamical systems (
C, A, B
) with
m
inputs and
p
outputs, with restricted static-state feedback, in other words with control laws of type
u = GFx + Gv
. We give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in [2] for the simple case
k = p \leq m
, where
k
denotes the number of blocks to be decoupled.