Almost disturbance decoupling with internal stability: frequency domain conditions

The problem is that of determining a dynamic measurement feedback which makes the H^∞-norm of the disturbance-input-to-regulated-output transfer matrix arbitrarily small while achieving internal stability. it is shown that the solvability condition in the frequency domain for this problem is a purely algebraic one and can be formulated in terms of a two-sided matrix matching equation involving polynomial system matrices. This is known to be a zero cancellation condition. A synthesis procedure for the compensator in the frequency domain is also given