Rational approximation in linear systems and control
type: Item
instance of: scholarly article
title: Rational approximation in linear systems and control
zbMATH Open document ID: 0967.30023
DOI: 10.1016/S0377-0427(00)00339-3
author: Adhemar Bultheel
author: B. De Moor
published in: Journal of Computational and Applied Mathematics
publication date: 2001-08-26T00:00:00Z
review text: It is possible to say that the paper is a ``oversurvey'' in the sense of giving no details but main ideas only from different large theories. The authors show how rational approximation appears by a natural way while solving problems from linear system theory. Let us give a list of considered problems: minimal partial realization, Hankel and \(H_2\) norm approximation of transfer functions, linear prediction (together with trigonometric moment problem, Nevanlinna-Pick interpolation and Nehari problem), \(H^{\infty}\) control, identification. Some recent generalizations are discussed too.
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 1533141
zbMATH Keywords: rational approximation
zbMATH Keywords: linear system theory
zbMATH Keywords: model reduction
zbMATH Keywords: identification
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
cites work: ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM
cites work: Q4856607
cites work: Q4012895
cites work: Interpolation of rational matrix functions
cites work: Padé-type approximation and general orthogonal polynomials
cites work: Laurent series and their Padé approximations
cites work: Q4223056
cites work: On several aspects of \(J\)-inner functions in Schur analysis
cites work: Padé techniques for model reduction in linear system theory: a survey
cites work: Linear prediction: Mathematics and engineering
cites work: Formal orthogonal polynomials and Hankel/Toeplitz duality
cites work: Linear algebra, rational approximation and orthogonal polynomials
cites work: A Convex Optimization Approach to the Rational Covariance Extension Problem
cites work: Schur parameters, factorization and dilation problems
cites work: Q4841316
cites work: Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences
cites work: Lossless inverse scattering, digital filters, and estimation theory
cites work: Q3838074
cites work: On a generalized Szegö- Levinson realization algorithm for optimal linear predictors based on a network synthesis approach
cites work: A look-ahead algorithm for the solution of general Hankel systems
cites work: All optimal Hankel-norm approximations of linear multivariable systems and theirL,∞-error bounds†
cites work: Matrix and operator valued functions. The Vladimir Petrovich Potapov memorial volume
cites work: Q4257499
cites work: On the partial realization problem
cites work: Q3247378
cites work: Anticausal stabilizing solution to discrete reverse-time Riccati equation
cites work: The area enclosed by the (oriented) Nyquist diagram and the Hilbert-Schmidt-Hankel norm of a linear system
cites work: The CF table
cites work: Algebraic methods for Toeplitz-like matrices and operators
cites work: Q5521815
cites work: Q3481150
cites work: Displacement Structure: Theory and Applications
cites work: Chain-scattering approach to \(H^ \infty\) control
cites work: Q4724470
cites work: Principal component analysis in linear systems: Controllability, observability, and model reduction
cites work: A unifying construction of orthonormal bases for system identification
cites work: Q4340908
cites work: The multiplicative structure of 𝐽-contractive matrix functions
cites work: Near-circularity of the error curve in complex Chebyshev approximation
cites work: Orthonormal polynomial vectors and least squares approximation for a discrete inner product
cites work: Q4366804
cites work: Q5794082
cites work: The prediction theory of multivariate stochastic processes. I. The regularity condition. - II. The linear predictor
Wikidata QID: Q127494004
Recommended article: Q4877780
Recommended article: Q4273636
Recommended article: Control of rational systems using linear-fractional representations and linear matrix inequalities
Recommended article: Approximate linearization of nonlinear control systems
Recommended article: Rational approximation of L/sub 1/ optimal controllers for SISO systems
Recommended article: Approximation with the output of linear control systems
Recommended article: Approximation methods of nonlinear control systems
Recommended article: Rational approximation of distributed parameter systems
Recommended article: On approximate linearization of nonlinear control systems
Recommended article: Further results on rational approximations of ℒ/sup 1/ optimal controllers
description: scientific article; zbMATH DE number 1533141