Input/Output Stabilization in the General TwoSided Model Matching Setup
(2012) In SIAM Journal of Control and Optimization 50(3). p.14131438 Abstract
 The problem of inputoutput stabilization in a general twosided 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 statespace formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding onesided 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 inputoutput stabilization in a general twosided 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 statespace formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding onesided 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 twosided stabilization problem is similar to its onesided 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:
http://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
 SIAM Publications
 external identifiers

 wos:000305961400015
 scopus:84865487639
 ISSN
 10957138
 DOI
 10.1137/100803304
 language
 English
 LU publication?
 yes
 id
 50d210628c014b7aa81723ea955e3822 (old id 3008053)
 date added to LUP
 20120821 09:03:20
 date last changed
 20180107 04:29:48
@article{50d210628c014b7aa81723ea955e3822, abstract = {The problem of inputoutput stabilization in a general twosided 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 statespace formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding onesided 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 twosided stabilization problem is similar to its onesided 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 = {10957138}, keyword = {model matching,stabilization,interpolation constraints,unstable,weights,bilateral Diophantine equation}, language = {eng}, number = {3}, pages = {14131438}, publisher = {SIAM Publications}, series = {SIAM Journal of Control and Optimization}, title = {Input/Output Stabilization in the General TwoSided Model Matching Setup}, url = {http://dx.doi.org/10.1137/100803304}, volume = {50}, year = {2012}, }