Almost non interacting control by measurement feedback

Consider a linear system $\Sigma$ that, apart from a control input and a measurement output, has two exogenous inputs and two exogenous outputs. Controlling such a system by means of a measurement feedback compensator $\Sigma_c$ 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 $\Sigma$ and any positive number e, is it possible to find $\Sigma_c$ such that the off-diagonal blocks of the closed loop transfer matrix, in a suitable norm, are smaller than e? For the solvability of this problem necessary and sufficient conditions will be derived. Keywords & Phrases: Almost non interacting control, measurement feedback, common solution to a pair of linear matrix equations