Equivalence Between Open-Loop and Closed-Loop Invariance for Infinite-Dimensional Systems: A Frequency Domain Approach

Abstract

In this paper the relation between various system invariance concepts is considered, and it is proved that open- and closed-loop invariance are equivalent concepts. Using this equivalence the author investigates the existence of the largest closed-loop invariant subspace, and derives necessary and sufficient conditions such that the largest open-loop invariant subspace is equal to the largest closed-loop invariant subspace. If this equality holds, then the solvability of the disturbance decoupling problem (DDP) is equivalent to the solvability of a meromorphic matrix equation.