Advertisement
Published in:
2015 | OriginalPaper | Chapter
State Space Formulas for a Suboptimal Rational Leech Problem II: Parametrization of All Solutions
Authors : A. E. Frazho, S. ter Horst, M. A. Kaashoek
Published in: Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
For the strictly positive case (the suboptimal case), given stable rational matrix functions
G
and
K
, the set of all
H
∞
solutions
X
to the Leech problem associated with
G
and
K
, that is,
G
(
z
)
X
(
z
) =
K
(
z
) and
$$ {\mathrm {sup}}_{{\mid z \mid}{\leq}{1}} {\parallel {X}{(z)} \parallel} \ {\leq} {1} $$
, is presented as the range of a linear fractional representation of which the coefficients are presented in state space form. The matrices involved in the realizations are computed from state space realizations of the data functions
G
and
K
. On the one hand the results are based on the commutant lifting theorem and on the other hand on stabilizing solutions of algebraic Riccati equations related to spectral factorizations.