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 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 nonzero, 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.

本文在具有可能的输入-输出馈通矩阵的系统的一般情况下，通过动态输出反馈来研究干扰解耦问题。特别地，我们旨在扩展基于自边界和自隐藏的几何条件，这使得能够解决解耦问题而无需本征空间计算。我们证明，与零馈通矩阵的情况完全一样，该解决方案最大程度地增加了闭环可分配特征值的数量。由于在此框架中，我们允许每个馈通矩阵都不为零，因此出现了反馈互连的适度性问题，这影响了可溶性条件的构造方式。但是，我们显示