Linear systems theory. A structural decomposition approach.
type: Item
instance of: scholarly article
title: Linear systems theory. A structural decomposition approach.
zbMATH Open document ID: 1087.93001
author: Zongli Lin
author: Ben M. Chen
author: Y. Shamash
published in: Control Engineering
publication date: 2005-06-08T00:00:00Z
review text: This book presents various canonical forms for linear systems in continuous and discrete time and shows how such decompositions, called structural decompositions, have an impact on various design and synthesis problems. The first three chapters provide the necessary background in linear algebra and linear systems theory (controllability/observability, stability, invertibility, zeros, geometric methods, output injection). The next four chapters deal with several structural decompositions (the ones related to stability, the ones related to controllability and/or observability). The cases of descriptor systems and proper systems are detailed. The bilinear transformation relates continuous and discrete versions. The rest of the book deals with applications of these results. First, it is shown how the decompositions are instrumental for system factorizations (cascade factorizations). Then pole and zero placement issues are addressed. A weaker form of asymptotic time-scale assignment is considered. The conceptually related problems of disturbance decoupling and \(H_\infty\) control are the subject of another chapter. Finally, a MATLAB toolkit for the algorithms is presented. A bibliography (164 items) and an index are offered at the end. This good book on linear systems theory, which shows nicely how geometry underlies important control issues, is recommended.
reviewed by: A. Akutowicz
Mathematics Subject Classification ID: 93-01
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93B12
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 2174323
zbMATH Keywords: canonical forms
zbMATH Keywords: structural decompositions
zbMATH Keywords: zeros
zbMATH Keywords: geometric methods
zbMATH Keywords: descriptor systems
zbMATH Keywords: bilinear transformation
zbMATH Keywords: pole and zero placement
zbMATH Keywords: disturbance decoupling
zbMATH Keywords: \(H_\infty\) control
describes a project that uses: Matlab
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2174323