Almost Disturbance Decoupling with Internal Stability: Frequency Domain Conditions

This note considers the almost disturbance decoupling problem with internal stability. 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 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 frequency domain is also given. © 1990 IEE