On a connection between spectral factorization and geometric control theory

A. Gombani, P. A. Fuhrmann

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We investigate here how the geometric control theory of Basile, Marro and Wonham can be obtained in a Hilbert space context, as the byproduct of the factorization of a spectral density with no zeros on the imaginary axis. We show how controlled invariant subspaces can be obtained as images of orthogonal projections of co-invariant subspaces onto a semi-invariant (Markovian) subspace of the Hardy space of square integrable functions analytic in the right half-plane. Output nulling subspaces are then related to a particular spectral factorization problem. A similar construction is presented for controllability subspaces, and a new algorithm for the computation of these subspaces is presented.

Original languageEnglish
Pages (from-to)824-859
Number of pages36
JournalInternational Journal of Control
Issue number11
StatePublished - 20 Jul 2002
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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