Non-interacting control by measurement feedback for outputs complete systems

In this paper we shall consider systems that in addition to a control input and a measurement output have two exogenous inputs and two exogenous outputs. Furthermore, we assume that the two exogenous outputs of these systems are complete, i.e. we assume that the state of these systems can be written as a linear combination of the two exogenous outputs. For this kind of systems we shall solve the problem of non interacting control by measurement feedback. That is, we shall derive necessary and sufficient conditions for the existence of a measurement feedback compensator such that the transfer matrix of the resulting closed loop system. when partitioned according to exogenous inputs and exogenous outputs, has off-diagonal blocks equal to zero