Topics in Multidimensional Linear Systems Theory

by Eva Zerz

Overview

The past few decades have witnessed an increasing interest in the field of multidimensional systems theory. This is concerned with systems whose trajectories depend not on one single variable (usually interpreted as time or frequency), but on several independent variables, such as the coordinates of an image.

The behavioural approach introduced by J. C. Willems provides a particularly suitable framework for developing a linear systems theory in several variables. The book deals with the classical concepts of autonomy, controllability, observability, and stabilizability. All the tests and criteria given are constructive in the sense that algorithmic versions may be implemented in modern computer algebra systems, using Gröbner basis techniques.

There is a close connection between multidimensional systems theory and robust control of one-dimensional systems with several uncertain parameters. The central link consists in the basic tool of linear fractional transformations. The book concludes with examples from the theory of electrical networks.

Product Details

ISBN-13:	9781852333362
Publisher:	Springer London
Publication date:	09/15/2000
Series:	Lecture Notes in Control and Information Sciences , #256
Edition description:	2000
Pages:	168
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Controllability of multidimensional systems.- Co-prime factorizations of multivariate rational matrices.- Stabilizability.- Strict system equivalence.- First order representations of multidimensional systems.- Linear fractional transformations.- Electrical networks.