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Input/Output Stabilization in the General Two-Sided Model Matching Setup

Kristalny, Maxim LU and Mirkin, Leonid (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:
author
organization
publishing date
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
SIAM Publications
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
2012-08-21 09:03:20
date last changed
2017-01-01 03:57:02
@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},
  keyword      = {model matching,stabilization,interpolation constraints,unstable,weights,bilateral Diophantine equation},
  language     = {eng},
  number       = {3},
  pages        = {1413--1438},
  publisher    = {SIAM Publications},
  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},
  volume       = {50},
  year         = {2012},
}