Feedback invariants via output injection
type: Item
instance of: scholarly article
title: Feedback invariants via output injection
zbMATH Open document ID: 1060.93028
author: A. Roca
author: Ion Zaballa
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: Two input-state systems are called feedback equivalent if there exists a basis transformation on the state space, a basis transformation on the input space, and a feedback which (together) transform the first system into the second one. The class of feedback equivalent input-state systems is characterized by the invariant factors and the minimal indices of the associated pencil. Here, the authors study the following problem: given a class of feedback equivalent input-state systems and the quadruple \((A,B,C,D)\), when does there exists an output injection \(K\) such that \((A+KC, B+KD)\) becomes an element of the equivalence class. This problem has a long history, see, e.g., \textit{I. Cabral, F. Silva} and \textit{I. Zaballa} [Linear Algebra Appl. 332--334, 447--458 (2001; Zbl 1049.93038)]. The novelty of this paper is that the underlying field is arbitrary, and thus may be finite.
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A22
zbMATH DE Number: 2083523
zbMATH Keywords: feedback equivalence
zbMATH Keywords: canonical structure
zbMATH Keywords: output injection
zbMATH Keywords: transformation
zbMATH Keywords: invariant factors
zbMATH Keywords: minimal indices
zbMATH Keywords: pencil
reviewed by: Hans Zwart
MaRDI profile type: Publication
full work available at URL: j.laa.2003.12.030
OpenAlex ID: W1987883052
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DOI: 10.1016/J.LAA.2003.12.030
description: scientific article; zbMATH DE number 2083523