Overlapping block-balanced canonical forms for various classes of linear systems
type: Item
instance of: scholarly article
title: Overlapping block-balanced canonical forms for various classes of linear systems
zbMATH Open document ID: 0947.93006
DOI: 10.1016/S0024-3795(98)10056-3
author: B. Hanzon
author: Raimund J. Ober
published in: Linear Algebra and its Applications
publication date: 2000-02-07T00:00:00Z
review text: Through the use of balanced realizations it has been possible to derive parameterizations and canonical forms for various classes of minimal linear systems of given dimension. A possible problem of these parameterization is that they are not overlapping. This could be a drawback for the application of balanced parameterizations in such areas as system identification, model reduction and optimization. It is the topic of this paper to derive overlapping parameterizations which are closely related to the existing balanced parameterizations. This is a highly specialized and carefully written paper. The results include both the single-input single-output case and the multivariable case.
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B20
zbMATH DE Number: 1370030
zbMATH Keywords: balanced realizations
zbMATH Keywords: canonical forms
zbMATH Keywords: overlapping parameterizations
reviewed by: Johannes W. Nieuwenhuis
MaRDI profile type: Publication
cites work: A transformation approach to stochastic model reduction
cites work: Q3859622
cites work: Q3254327
cites work: On Sigma-lossless transfer functions and related questions
cites work: All optimal Hankel-norm approximations of linear multivariable systems and theirL,∞-error bounds†
cites work: Q3995538
cites work: On the differentiable manifold of fixed order stable linear systems
cites work: A new balanced canonical form for stable multivariable systems
cites work: Constructive algebra methods for the \(L_ 2\)-problem for stable linear systems
cites work: Overlapping Block-Balanced Canonical Forms and Parametrizations: The Stable SISO Case
cites work: Moduli and canonical forms for linear dynamical systems II: The topological case
cites work: A new set of invariants for linear systems--Application to reduced order compensator design
cites work: Balanced forms: Canonicity and parameterization
cites work: Perturbation theory for linear operators.
cites work: Q4850020
cites work: Q3342413
cites work: Principal component analysis in linear systems: Controllability, observability, and model reduction
cites work: Balanced realizations: canonical form, parametrization, model reduction
cites work: Balanced Parametrization of Classes of Linear Systems
cites work: Q4892191
cites work: Q4308999
cites work: A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds
cites work: Model reduction via balanced state space representations
cites work: On diffeomorphisms between classes of linear systems
full work available at URL: s0024-3795(98)10056-3
OpenAlex ID: W2037371917
description: scientific article; zbMATH DE number 1370030