Self-Bounded Subspaces for Nonstrictly Proper Systems and Their Application to the Disturbance Decoupling With Direct Feedthrough Matrices

In this paper, the concept of self-bounded controlled invariance is extended to nonstrictly proper systems. Moreover, its use in connection with the disturbance decoupling problem with internal stability is investigated in the case where the feedthrough matrices from the control input and from the disturbance to the output to be decoupled are possibly nonzero.