Polynomial and rational matrices. Applications in dynamical systems theory
type: Item
instance of: scholarly article
title: Polynomial and rational matrices. Applications in dynamical systems theory
zbMATH Open document ID: 1114.15019
published in: Communications and Control Engineering
publication date: 2006-12-20T00:00:00Z
review text: It is an excellent book for polynomial and rational matrices and its applications in Dynamical Systems Theory, written by a very well-known scientist in the field of control theory. The book can be used either as a reference for researchers in the field of control theory and circuit theory or for teaching for undergraduates or postgraduates in electrical engineering, electronics, mechatronics and computer engineering. The book is an extended English version of its preceding Polish edition. Apart from the theory, the book includes many illustrative examples that make the theory more clear to the reader. However, the book does not contain enough results as concerns the structure of polynomial and rational matrices at \(s=\infty \) or a specific region \(\Lambda \subseteq \mathbb{C} \cup \left\{ \infty \right\} \), and the respective applications of this specific structure i.e. proper (or proper and stable) solutions of polynomial matrix diophantine equations. The monograph consists of eight chapters, an appendix and a list of references. Chapter 1 is devoted to the structure of polynomial matrices. It covers topics on polynomial matrices such as: elementary operations, division, equivalence, canonical forms, invariants, greatest common divisor, least common multiple, special kind of matrices etc. Chapter 2 starts with some basic definitions and operations of rational functions and matrices. Then, algebraic methods are proposed for the computation of the right (left) matrix fraction description (MFD) and the McMillan canonical form of a rational matrix. By using these methods, the synthesis problem of computing a regulator for a given plant is solved. Chapter 3 starts with a definition of normal rational matrices. Then, it studies the following properties of normal matrices: a) which is the form of the MFD of a normal rational matrix, b) under what conditions the sum, the product and the inverse of normal matrices are normal matrices, c) how a normal matrix can be deco…
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93-01
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 15-01
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A06
zbMATH DE Number: 5080872
zbMATH Keywords: polynomial matrices
zbMATH Keywords: rational matrices
zbMATH Keywords: normal matrices
zbMATH Keywords: realization
zbMATH Keywords: singular systems
zbMATH Keywords: cyclic normal systems
zbMATH Keywords: polynomial matrix equations
zbMATH Keywords: observers
zbMATH Keywords: positive linear systems
zbMATH Keywords: canonical forms
zbMATH Keywords: Sylvester equation
zbMATH Keywords: Lyapunov equation
author: Tadeusz Kaczorek
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5080872