Disturbance decoupling by behavioral feedback for linear differential-algebraic systems

We study disturbance decoupling for linear differential-algebraic systems which are not necessarily regular. Compared to previous approaches, where state feedback is used, we use the concept of behavioral feedback which allows to study a larger class of systems. We derive geometric characterizations for solvability of the disturbance decoupling problem following the classical approach. Exploiting the freedom in the choice of the behavioral feedback we show that whenever disturbance decoupling can be achieved by behavioral feedback we may additionally achieve autonomous zero dynamics. Finally we solve Lebret's twenty year old open problem concerning disturbance decoupling with output uniqueness using behavioral feedback.