Almost disturbance decoupling with bounded peaking

In this paper we study a generalization of the almost disturbance decoupling problem by state feedback. Apart from approximate decoupling from the external disturbances to a first to-be-controlled output, we require a second output to be uniformly bounded with respect to the accuracy of decoupling. We also study the situation in which additionally we require the closed loop system to be internally stable. These problems are studied using the geometric approach to linear systems. We introduce some new almost controlled invariant subspaces and study their geometric structure. Necessary and sufficient conditions for the solvability of the above problems are then formulated in terms of these almost controlled invariant subspaces.