Disturbance decoupling by measurement feedback with stability for infinite-dimensional systems

The concepts of controllability and stabilizability subspaces are extended to infinite-dimensional linear systems. Under certain assumptions one obtains a nice generalization of the finite-dimensional theory, and, by dualizing, similar results are obtained for the concepts of complementary observability and complementary detectability subspaces. These concepts are used to solve the infinite-dimensional version of the disturbance-decoupling problem, the disturbance-decoupled estimation problem and the disturbance-decoupling problem with measurement feedback, all requiring various stability requirements. The solution is in terms of geometric concepts such as (A, B)- and (C,A)- invariant subspaces and controllability and complementary observability subspace