Feedback block decoupling and infinite structure of linear systems

Abstract

Using factorizations at infinity of the transfer matrix, two interesting necessary and sufficient conditions arc obtained for the block decoupling problem of linear systems by state feedback and a constant non-singular input transformation. These conditions are expressed in a very simple way in terms of integers which are feedback invariants for the system under consideration. These feedback invariants are related either to the system infinite structure, or to the reachability indices of the feedback reduced system