Input/Output Stabilization in the General Two-Sided Model Matching Setup
(2012) In SIAM Journal of Control and Optimization 50(3). p.1413-1438- Abstract
- The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH infinity. Then, recent results on bilateral Diophantine equations are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding one-sided stabilization, where no Sylvester equations are required. It is shown that imposing a mild simplifying assumption is instrumental in obtaining convenient parameterization of all stabilizing solutions, which... (More)
- The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH infinity. Then, recent results on bilateral Diophantine equations are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding one-sided stabilization, where no Sylvester equations are required. It is shown that imposing a mild simplifying assumption is instrumental in obtaining convenient parameterization of all stabilizing solutions, which is affine in a single RH infinity parameter. This demonstrates that if the aforementioned assumption is imposed, the general two-sided stabilization problem is similar to its one-sided counterpart in the sense that the constraints imposed by a stability requirement can be resolved without increasing problem complexity. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3008053
- author
- Kristalny, Maxim LU and Mirkin, Leonid
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- model matching, stabilization, interpolation constraints, unstable, weights, bilateral Diophantine equation
- in
- SIAM Journal of Control and Optimization
- volume
- 50
- issue
- 3
- pages
- 1413 - 1438
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000305961400015
- scopus:84865487639
- ISSN
- 1095-7138
- DOI
- 10.1137/100803304
- language
- English
- LU publication?
- yes
- id
- 50d21062-8c01-4b7a-a817-23ea955e3822 (old id 3008053)
- date added to LUP
- 2016-04-01 10:50:53
- date last changed
- 2024-01-07 02:36:18
@article{50d21062-8c01-4b7a-a817-23ea955e3822,
abstract = {{The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH infinity. Then, recent results on bilateral Diophantine equations are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding one-sided stabilization, where no Sylvester equations are required. It is shown that imposing a mild simplifying assumption is instrumental in obtaining convenient parameterization of all stabilizing solutions, which is affine in a single RH infinity parameter. This demonstrates that if the aforementioned assumption is imposed, the general two-sided stabilization problem is similar to its one-sided counterpart in the sense that the constraints imposed by a stability requirement can be resolved without increasing problem complexity.}},
author = {{Kristalny, Maxim and Mirkin, Leonid}},
issn = {{1095-7138}},
keywords = {{model matching; stabilization; interpolation constraints; unstable; weights; bilateral Diophantine equation}},
language = {{eng}},
number = {{3}},
pages = {{1413--1438}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal of Control and Optimization}},
title = {{Input/Output Stabilization in the General Two-Sided Model Matching Setup}},
url = {{http://dx.doi.org/10.1137/100803304}},
doi = {{10.1137/100803304}},
volume = {{50}},
year = {{2012}},
}