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Applied multidimensional systems theory. (English) Zbl 0574.93031

Van Nostrand Reinhold Electrical/Computer Science and Engineering Series. New York - London: Van Nostrand Reinhold Co. (ISBN 978-0-442-27214-2). xvi, 411 p. (1982).
This book brings together recent work in multidimensional linear systems theory. This work has applications in such areas as image processing, seismic signal processing, and radar. The first two chapters deal with properties of multivariate polynomials. These chapters are a good introduction to the theory of rational functions and polynomial matrices. There are also chapters on stability and realizability. The final chapter discusses a variety of applications including digital filtering in a finite field and Volterra series. The chapters on stability are perhaps the clearest available on the subject. Each chapter has a set of exercises and a rather complete list of references. The book would make an excellent text for an introductory graduate level course in multidimensional systems.
The reviewer’s only criticism of the book is that there is no introductory chapter to motivate the study of multivariate polynomials. A reader wishing to get a feeling for some of the problems in multidimensional systems theory would have to start with Chapter 3.

MSC:

93C35 Multivariable systems, multidimensional control systems
93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory
93C05 Linear systems in control theory
26C05 Real polynomials: analytic properties, etc.
26C15 Real rational functions
41A20 Approximation by rational functions
93B15 Realizations from input-output data
93Dxx Stability of control systems
93E11 Filtering in stochastic control theory
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