Almost invariant subspaces: An approach to high gain feedback design--Part II: Almost conditionally invariant subspaces

In Part I of this paper, almost controlled invariant subspaces were studied. In this part we will consider their duals, the almost conditionally invariant subspaces. These concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem. Finally, we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if: 1) almost disturbance decoupling by state feedback, and 2) almost disturbance decoupled estimation of the to-be-controlled output are both possible.