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

Fixed poles of the disturbance decoupling problem by dynamic output feedback for biproper systems