Almost non-interacting control by measurement feedback

Consider a linear system S that, apart from a control input and a measurement output, has two exogeneous inputs and two exogenous outputs. Controlling such a system by means of a measurement feedback compensator Sc results in a closed loop system with two inputs and two outputs. Hence, the closed loop transfer matrix can be partitioned as a two by two block matrix. The problem addressed in this paper consists of the following. Given S and any positive number ge, is it possible to find Sc such that the off-diagonal blocks of the closed transfer matrix, in a suitable norm, are smaller than e? For the solvability of this problem necessary and sufficient conditons will be derived.