Explicit solvability conditions for a class of disturbance decoupling problems with static measurement feedback

We consider two well-known disturbance decoupling problems. We first derive a checkable necessary and sufficient condition under which the disturbance decoupling problem with static measurement feedback (DDPKM) is solvable for a class of multi-input and multi-output linear time-invariant systems, which have a left invertible transfer matrix function from the control input to the controlled output. The paper also constructs and parametrizes explicitly the set of all solutions that solve the above mentioned DDPKM. This set is then used to solve the disturbance decoupling problem with static measurement feedback and with internal stability