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:
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Mathematical models;
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Introduction to state space theory;
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Stability theory;
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Perturbation theory; and
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Uncertain spaces.
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.