Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness

Kybernetes

ISSN: 0368-492X

Article publication date: 1 October 2005

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Keywords

Citation

Howard, W.R. (2005), "Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness", Kybernetes, Vol. 34 No. 9/10, pp. 1659-1659. https://doi.org/10.1108/03684920510614885

Publisher

:

Emerald Group Publishing Limited

Copyright © 2005, Emerald Group Publishing Limited


This is a book that sets out the mathematical foundations of systems theory and as such presents the reader with the first volume of a self contained introduction to the field.

This volume is written by Drs Diederich Hinrichsen of Bremen, Germany and Anthony Pritchard of the University of Warwick, UK. In particular, it is concerned with outlining the mathematical basis for systems theory that so many cyberneticians and systemists accept exists, but have no real insight into how it could be explained. The text takes up the challenge and aims to produce the author's explanations in a comprehensive, complete and, of most importance, mathematically rigorous manner.

To do this they have produced a contribution that is both an introductory text and also a sound reference source. It also includes an appendix that covers linear algebra; complex analysis; convolutions and transforms; and linear operators.

The main contents covers the analysis of dynamical systems and provides examples and illustrations (some 200) which certainly help in the understanding of the mathematical constructions that are discussed. The important topics introduced include:

  • Mathematical models;

  • Introduction to state space theory;

  • Stability theory;

  • Perturbation theory; and

  • Uncertain spaces.

A guide to readers who want to know whether their mathematical background suffices is given by the publishers who believe “that it is accessible to mathematics students after two years of mathematics and to graduate engineering students specialising in mathematical systems theory”. This is helpful, particularly to researchers who have followed a multidisciplinary path through both systems and cybernetics. Many readers from these fields may not wish to follow the rigorous mathematical approach to their studies, but this book does give those engaged in systems research a good and clear introduction to the mathematical view of their field.

It is also worth knowing that a second volume will be devoted to control and if the same comprehensive and detailed exposition ensues, it will be well worth considering.

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