- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Bezout Equations for Stable Rational Matrix Functions:...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Bezout Equations for Stable Rational Matrix Functions: The Least Squares Solution and Description of all Solutions Kaashoek, Rien
Description
This talk concerns the corona type Bezout equation $G(z)X(z)=I_p$, $z$ in $BD$. The function $G$ is the given function and $X$ is the unknown. Both functions are stable rational matrix functions, $G$ is of size $p\times q$ and $X$ of size $q\times p$, and $I_p$ stands for the $p\times p$ identity matrix. Here \emph{stable} means that the poles of the rational matrix functions involved are all outside the closed unit disc, and hence the entries of these matrix functions are $H^\infty$- functions. We shall use state space techniques from mathematical system theory to obtain necessary and sufficient conditions for existence of solutions. Furthermore, we derive an explicit formula for the least squares solution and an explicit description of all solutions, all in terms of a state space realization of the given function $G$. The state space formula for the least squares solution is easy to use in Matlab, and it shows that the McMillan degree of this solution is less than or equal to the McMillan degree of $G$. The talk is based on joint work with Art Frazho (Purdue University) and Andre Ran (VU Amsterdam).
Item Metadata
Title |
Bezout Equations for Stable Rational Matrix Functions: The Least Squares Solution and Description of all Solutions
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2017-07-09T11:00
|
Description |
This talk concerns the corona type Bezout equation $G(z)X(z)=I_p$, $z$ in $BD$. The function $G$ is the given function and $X$ is the unknown. Both functions are stable rational matrix functions, $G$ is of size $p\times q$ and $X$ of size $q\times p$, and $I_p$ stands for the $p\times p$ identity matrix. Here \emph{stable} means that the poles of the rational matrix functions involved are all outside the closed unit disc, and hence the entries of these matrix functions are $H^\infty$- functions. We shall use state space techniques from mathematical system theory to obtain necessary and sufficient conditions for existence of solutions. Furthermore, we derive an explicit formula for the least squares solution and an explicit description of all solutions, all in terms of a state space realization of the given function $G$. The state space formula for the least squares solution is easy to use in Matlab, and it shows that the McMillan degree of this solution is less than or equal to the McMillan degree of $G$. The talk is based on joint work with Art Frazho (Purdue University) and Andre Ran (VU Amsterdam).
|
Extent |
31 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Vrije Universiteit
|
Series | |
Date Available |
2018-01-05
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0362887
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International