  This paper investigates the disturbance decoupling problem by dynamic output
feedback in the general case of systems with possible input-output feedthrough
matrices. In particular, we aim to extend the geometric condition based on
self-boundedness and self-hiddenness, which as is well-known enables to solve
the decoupling problem without requiring eigenspace computations. We show that,
exactly as in the case of zero feedthrough matrices, this solution maximizes
the number of assignable eigenvalues of the closed-loop. Since in this
framework we are allowing every feedthrough matrix to be non-zero, an issue of
well-posedness of the feedback interconnection arises, which affects the way
the solvability conditions are structured. We show, however, that the further
solvability condition which originates from the problem of well-posedness is
well-behaved in the case where we express such condition in terms of self
bounded and self hidden subspaces.
