Abstract
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 language | English |
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Pages (from-to) | 824-859 |
Number of pages | 36 |
Journal | International Journal of Control |
Volume | 75 |
Issue number | 11 |
DOIs | |
State | Published - 20 Jul 2002 |
Externally published | Yes |
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications