Preface to the Revised Edition

Preface to the Revised Edition

Preface to the Revised Edition When the first edition of this book, (formerly titled Dynamical Systems and their Applications: Linear Theory) was pub...

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Preface to the Revised Edition

When the first edition of this book, (formerly titled Dynamical Systems and their Applications: Linear Theory) was published in 1977, it presented a reasonably thorough account of the major ideas and results of linear system theory circa mid-1970s. The past decade has witnessed an explosion of interest in mathematical system theory with major advances in the understanding of systems governed by functional differential equations, n-d systems, system identification, numerical methods, and frequency-domain techniques, not to mention the creation of an elegant and comprehensive algebraic and geometric theory of linear systems. And this is just for linear systems; much more can be said about new results in bifurcation theory, chaos, fractals, and other nonlinear phenomena, some of which is treated in my volume, Nonlinear System Theory (Academic Press, 1985), a companion to the present work. The task of doing justice to this impressive body of new work in a hundred pages or less was an imposing one, and one which ultimately required many compromises. Since a detailed account of all major developments was totally out of the question, I decided to treat a few topics in some depth and then to incorporate most of the remaining results by way of augmented references and problems in the earlier chapters. Thus, the current volume includes chapter-length expositions of the algebraic and geometric theory of linear systems (Chapter 9) and the theory of infinite-dimensional systems (Chapter 10). The other topics are interwoven into Chapters 1-8, together with the correction of a number of unfortunate typos, numerical errors and, in one or two places, just plain erroneous results that marred the first edition of this book. xi

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PREFACE TO THE REVISED EDITION

At this time, I would like to record my thanks to numerous colleagues, friends and students who were kind enough to show me the error of my ways in the book’s first edition and who served as a source of inspiration to prepare this much more comprehensive work. Their efforts and support have shaped both the content and form of this volume. John L. Casti Vienna January 1986.