Abstract
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.
Dedicated to Lev A. Sakhnovich on the occasion of his eightieth birthday with admiration
Mathematics Subject Classification (2010). Primary 47A57; Secondary 47A68, 93B15, 47A56.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Frazho, A.E., ter Horst, S., Kaashoek, M.A. (2015). State Space Formulas for a Suboptimal Rational Leech Problem II: Parametrization of All Solutions. In: Alpay, D., Kirstein, B. (eds) Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes. Operator Theory: Advances and Applications(), vol 244. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10335-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-10335-8_8
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-10334-1
Online ISBN: 978-3-319-10335-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)