Polynomial characterizations of (H,F)-invariant subspaces with applications
type: Item
instance of: scholarly article
title: Polynomial characterizations of (H,F)-invariant subspaces with applications
zbMATH Open document ID: 0598.15014
DOI: 10.1016/0024-3795(86)90231-4
author: B. George
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: Let Z be a \(p\times m\) strictly proper transfer matrix in polynomial fractional representation \(Z=PQ^{-1}R+W\). The author obtains polynomial characterizations for (H,F)-invariant subspaces associated with the realization \(\Sigma (P,Q,R,W)=(F,G,H,X_ Q)\) [cf. \textit{P. Fuhrmann}, J. Franklin Inst. 301, 521-540 (1976; Zbl 0332.93001)]. For full rank transfer matrices, he describes in terms of factors of the polynomial system matrix the smallest unobservability subspace containing Im G and largest reachability subspace in Ker H. Moreover he applies the obtained results to the stabilization problem with measurement feedback and to the disturbance decoupling problem with measurement feedback. In both cases he first gives the polynomial solvability conditions and, with the help of the characterizations developed for (H,F)-invariant subspaces obtains geometric interpretations.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 3964062
zbMATH Keywords: transfer matrix
zbMATH Keywords: polynomial fractional representation
zbMATH Keywords: invariant subspaces
zbMATH Keywords: polynomial system matrix
zbMATH Keywords: unobservability subspace
zbMATH Keywords: reachability subspace
zbMATH Keywords: stabilization problem
zbMATH Keywords: measurement feedback
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90231-4
OpenAlex ID: W2072267052
cites work: Disturbance localization and output deadbeat control through an observer in discrete-time linear multivariable systems
cites work: A Polynomial Characterization of $(\mathcal{A},\mathcal{B})$-Invariant and Reachability Subspaces
cites work: Algebraic system theory: An analyst's point of view
cites work: On strict system equivalence and similarity†
cites work: Duality in polynomial models with some applications to geometric control theory
cites work: A study of (A, B) invariant subspaces via polynomial models
cites work: Causal Factorization and Linear Feedback
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: Further results on polynomial characterizations of (&lt;tex&gt;F, G&lt;/tex&gt;)-invariant and reachability subspaces
cites work: Skew-prime polynomial matrices: The polynomial-model approach
cites work: Compensator synthesis using (C,A,B)-pairs
cites work: Linear multivariable systems
cites work: Geometric state-space theory in linear multivariable control: A status report
cites work: Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
description: scientific article; zbMATH DE number 3964062