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© 2005

Mathematical Systems Theory I

Modelling, State Space Analysis, Stability and Robustness

  • Comprehensive coverage of an important field in applied mathematics

Textbook

Part of the Texts in Applied Mathematics book series (TAM, volume 48)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Diederich Hinrichsen, Anthony J. Pritchard
    Pages 1-72
  3. Diederich Hinrichsen, Anthony J. Pritchard
    Pages 73-192
  4. Diederich Hinrichsen, Anthony J. Pritchard
    Pages 193-368
  5. Diederich Hinrichsen, Anthony J. Pritchard
    Pages 369-516
  6. Diederich Hinrichsen, Anthony J. Pritchard
    Pages 517-713
  7. Back Matter
    Pages 715-804

About this book

Introduction

This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way.

This first volume is devoted to the analysis of dynamical systems with emphasis on problems of uncertainty, whereas the second volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. It is accessible to mathematics students after two years of mathematics and graduate engineering students specializing in mathematical systems theory. The reader is gradually brought to the frontiers of research in stability and robustness analysis. As such the book will be useful for established researchers in systems theory as well as mathematicians and engineers interested in the mathematical foundations of systems and control.

From the reviews:

"This textbook on finite-dimensional time-invariant linear systems theory ... links up with the extensive research contributions of the authors, geared towards developing a spectral theory for uncertain systems. ... is bound to become a standard textbook and reference in its area." M. Kawski, Mathematical Reviews, 2005

"... the content ranges from rigorous proofs of basic results in linear systems theory to new results on the research frontier. In that sense, the book also serves as a valuable research reference." W.J. Satzer, MathDL, May, 2005

"I heartily recommend this book as a remarkably complete reference for researchers doing theoretical work involving linear systems. The book is a unique compilation of the mathematics underlying the field, and I look forward to seeing the authors' treatment of synthesis problems in the second volume." Brian Ingalls, IEEE Control Systems Magazine, April 2006

"MST-1 can be properly deemed an essential addition to the personal library of any researcher in systems theory. ...the authors indicate that MST-I was developed over a twenty-year period and the enormous effort that they have invested in writing the book is readily apoparent. MST-I is a superb exposition of advanced aspects of linear systems theory and is highly recommended for graduate students and researchers who have some prior background in control-systems and who have specific interests in problems of stability, robustness, and uncertainty. If the authors are able to maintain their high standards of exposition through the promised second volume, then MST-I and -II are destined to be placed among the pre-eminent authoritative references for the area of controlled dynamical systems." K.A. Grasse, IEEE Trans. Automatic Control 51, April 2006

"... This book is one of the best books on the subject." A.O. Ignatyev, Zentralblatt MATH 1074 :l

Keywords

linear optimization linear systems modelling perturbation theory stability theory systems theory uncertain systems and robustness

Authors and affiliations

  1. 1.Fachbereich Mathematik und InformatikUniversität BremenBremenGermany
  2. 2.Institute of Mathematics University ofWarwickCoventryUnited Kingdom

Bibliographic information

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Reviews

From the reviews:

"This textbook on finite-dimensional time-invariant linear systems theory … links up with the extensive research contributions of the authors, geared towards developing a spectral theory for uncertain systems. … Each section ends with a detailed list of notes and references … . this textbook provides a comprehensive introduction to linear systems theory with clear focus on robustness and uncertainty. … is bound to become a standard textbook and reference in its area. We are looking forward to the second volume."

Matthias Kawski, Mathematical Reviews, 2005j

"This book has been written by famous mathematicians. [...] A lot of new examples, explanations and figures were added, making this book accessible and well readable for engineers as well as mathematicians. This book is one of the best books on the subject."

Alexander O. Ignatyev, MATH Database 1931. 2006

"Mathematical Systems Theory I … provides a detailed and rigorous mathematical development of finite-dimensional, time-invariant linear systems. … The intended audience for this text is advanced undergraduates and first or second year graduate students. The authors suggest that several courses based on their book are possible depending on the selection of chapters. Indeed, the content ranges from rigorous proofs of basic results in linear systems theory to new results on the research frontier. In that sense, the book also serves as a valuable research reference." (William J. Satzer, MathDL, May, 2005)

"The book is … well written and well organized. … MST-I can be properly deemed an essential addition to the personal library of any researcher in systems theory. … MST-I is a superb exposition of advanced aspects of linear systems theory and is highly recommended for graduate students and researchers who have some prior background in control-systems theory and who have specific interests in problems of stability, robustness, and uncertainty." (K. A. Grasse, Transactions on Automatic Control, Vol. 51 (4), April, 2006)

"This book provides a thorough description of the theory of linear systems. … I heartily recommend this book as a … reference for researchers doing theoretical work involving linear systems. … There is no doubt that parts of the text could be successfully used for a graduate course in a mathematics program … . The book is a welcome addition to the library of work on systems theory and will no doubt serve as a valuable reference in many studies." (Brain Ingalls, Control Systems Magazine, April, 2006)

"This textbook contains a rigorous and detailed mathematical treatment of the basic elements of finite-dimensional time-invariant linear systems. … This volume is a comprehensive introduction to linear systems theory with clear focus on robustness and uncertainty. It can be used as a textbook for mathematics students after two years of study and also to engineering students with a good mathematical background. … it can be recommended for researchers as well as mathematicians and engineers interested in systems theory ." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 75, 2009)