Equivalence between open-loop and closed-loop invariance for infinite-dimensional systems: A frequency domain approach

Hans Zwart*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1175-1199
Number of pages25
JournalSIAM journal on control and optimization
Issue number5
Publication statusPublished - 1 Jan 1988
Externally publishedYes


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