On the assignability of infinite root loci in almost disturbance decoupling

Abstract

In this paper, we investigate in detail the almost disturbance decoupling problem with state feedback. An alternative proof of the sufficiency part of the original result by Willoms (1981) on this problem, requiring the construction of a sequence of feedback matrices, is given. It is shown that one can achieve almost disturbance decoupling by letting some of the closed loop eigenvalues run to infinity according to a spatial arrangement determined by the infinite zero structure. The proofs of our results use the fact that almost controllability subspaces can be approximated by controlled invariant subspaces. Our results on the closed-loop eigenstructure are stated in terms of such approximating sequences. We also prove a generalization of a theorem by Wonham (1979), used in the context of minimal order observer design.