This paper deals with the row-by-row decoupling problem (known as the Morgan problem)
with static state feedback. The solution of this problem is well known when some artificial constraints on the feedback laws are imposed (such as regular input transformations or restricted state feedbacks). However, in its most general setting;the problem remains unsolved.
Section 3 is devoted to some preliminary results. We then give in Section 4 the sufficient condition of solvability (Theorem 4.1) in the particular case when the order of the infinite zero of each row is equal to 1 and we show how this result can be used in the general situation (Theorem 4.2). Finally, we consider in Section 5 the particular case of systems having 2 outputs. It is then shown in Corollary 5.1 that our sufficient condition turns out to be also necessary in the particular case of systems having 2 outputs and 3 inputs. The paper is written within the state space approach.
We provide here a new sufficient condition of its solvability. The fact that this condition turns out to be also necessary in the particular case of systems having 2 outputs and 3 inputs enforces ifs interest.
Notation, basic concepts, problem setting