Realization theory of discrete-time dynamical systems.
type: Item
instance of: scholarly article
title: Realization theory of discrete-time dynamical systems.
zbMATH Open document ID: 1103.93004
author: Tsuyoshi Matsuo
author: Yasumichi Hasegawa
published in: Lecture Notes in Control and Information Sciences
publication date: 2003-11-11T00:00:00Z
review text: The objective of the book is to develop a realization theory for discrete-time non-linear systems in a general approach. The first author has constructed such a theory for non-linear continuous-time systems in [\textit{T. Matsuo}, Realization Theory of Continuous-Time Dynamical Systems, Lecture Notes in Control and Information Sciences, 32 (1981)], using as a starting point Kalman's algebraic theory for linear systems. The present monograph studies the realization theory for the discrete-time counterparts of the continuous-time General Dynamical Systems, Linear Representation Systems and Affine Dynamical Systems presented in the book quoted above and extends this theory to some special sub-classes called Pseudo Linear Systems, Almost Linear Systems and So-called Linear Systems (which include the category of Linear Systems). The monograph contains eight chapters and a suitable list of references. The chapters 3-10 have two parts: the first part presents the notions, the main results, the historical notes and the concluding remarks; the second part is an appendix which completes the list of definitions or theorems and contains the proofs of the mentioned results. The introductory Chapter 1 presents the aim and the structure of the book, as well as the inclusion diagram of different sub-classes of dynamical systems and automata. Chapter 2 collects the basic definitions necessary to the concept of input/output map. The free-monoid over an alphabet \(U\) is said to be a {concatenation monoid} \(\Omega\); the concatenation of two words \(\omega_{1}\) and \(\omega_{2}\) is denoted by \(\omega_{2}| \omega_{1}\) and \(| \omega| \) denotes the length of the word \(\omega\). For a set \(Y\), an { input/output relation} is defined as a map \(A^{\#}:\Omega\rightarrow F_{S}(\mathcal{N},Y):=\{\gamma:[0,n]\subset\mathbb{N}\rightarrow Y| \;\text{for some}\;n\in\mathbb{N}\}\). If \(A^{\#}(\omega_{2}| \omega_{1})(n)= A^{\#}(\omega_{3}| \omega_{1})(n),\;0\leq n\leq| \omega| \) for any …
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 2002748
zbMATH Keywords: realizations
zbMATH Keywords: non-linear systems
zbMATH Keywords: discrete-time systems
zbMATH Keywords: general dynamical systems
zbMATH Keywords: input-output map
zbMATH Keywords: concatenation monoid
MaRDI profile type: Publication
full work available at URL: b12094
OpenAlex ID: W2486650045
DOI: 10.1007/B12094
description: scientific article; zbMATH DE number 2002748