Transfer Matrix Approach to the Disturbance Decoupling Problem

Abstract In this paper the disturbance decoupling problem is considered from a transfer matrix point of view. Conditions for the existence of output feedback solutions are given. This problem amounts to solve the matrix equation AXB=C over the ring of proper rational functions. It will be shown that the infinite structure plays a key role in this problem. A generalization of previous results is obtained in a direct way without requiring geometric arguments. Some interesting particular cases will be pointed out as well as some possible extensions to stable synthesis.