Book Review - Linear State-Space Systems

Linear State-Space Systems Aplevich, Dwight J. (John Wiley, 1999)

£73.5, ISBN 0-471-24133-4, 0 pages

Publisher's Description

Reviewer

Professor David Fisk, , Imperial College London.

Summary Sentence

Well worth considering as a succinct modern well laid out text for mathematically competent engineering undergraduates, but its price suggests a hardback edition for the library rather than the backpack

Audience

The audience are final year undergraduates in a mathematically rich light current electrical engineering course, or first year post graduates. The text is clear and well fitted to this audience.

Content

The book gives an overview of the matrix algebra of linear dynamic systems. It covers the whole field in a modern approach that ranges from system identification to system stability. It does assume a mature approach to mathematics by the student, including for example the concepts of fields and rings. The topic of linear state space systems is not a subject with firm boundaries and some selection has had to be made by the author to keep the book concise. The approach of this book is to take linear systems as a self-contained topic. As a consequence topics are touched upon that are often dealt with more fully on other courses. For example some courses might treat optimal control or system stability as a self-standing theme where linear systems are only a subset or approximation of more general engineering problems. Lyapunov is usually handled in courses on the dynamics of non-linear systems, but this book brings in some of its theorems in the discussion of stability of linear systems. The heuristic advantage is that the book deals with (nearly always!) tractable problems, and gives the subject a sense of completeness.

One slight deviation from common practice is the use of central chapters on formal matrix theory. Some students may find the journey through these chapters a little parched of engineering content before they reach the other side and the chapters on stability. However there are also some useful ‘comments’ where the author helps relate the significance of a result or definition to practice. Few books would remind the reader that the determinant is better left as a theoretical concept rather than one needing numerical solution!

The examples usefully reflect access to MATLAB as a teaching resource. A somewhat surprising omission was any discussion of noisy signals in linear systems.

Style and Format

There are two extremes of textbook in this field, either an uncompromising mathematical text with rigorously formal notation, or a numerical recipes toolbox. This book aims for the middle ground. The book is attractively laid out - no small accomplishment for a text on matrices.

General Comments

The book is clearly based on a sequence of lectures. If this lecture plan matches requirements, this is an excellent concise textbook. The text has a nice crisp modern feel about it, which is a relief from some older textbooks. Special features include algorithms for system identification and minimisation of rank. There is a discussion of stability, though only a short discussion of optimal control of linear systems.

In other engineering disciplines state space ideas are often introduced without the linear restriction, or introduced earlier in the course. Probably the book fits best in an undergraduate course in which there has already be a preliminary skirmish with linear algebra and its applications, which has filtered out students who have other aptitudes. This book is intended to take ideas to a professional level, particularly for those specialising in linear as opposed to general systems. There are examples from various engineering fields, but the choice of material ultimately suggests an audience of light current engineering undergraduates. There is no soft back edition and so it may be more appropriate as an addition to the library.

In this Section: