Mathematical Systems Theory I
Modelling, State Space Analysis, Stability and Robustness
Authors: Hinrichsen, Diederich, Pritchard, Anthony J.
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 About this Textbook

This book presents the mathematical foundations of systems theory in a selfcontained, 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 finitedimensional timeinvariant 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
"MST1 can be properly deemed an essential addition to the personal library of any researcher in systems theory. ...the authors indicate that MSTI was developed over a twentyyear period and the enormous effort that they have invested in writing the book is readily apoparent. MSTI 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 controlsystems 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 MSTI and II are destined to be placed among the preeminent 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
 Reviews

From the reviews:
"This textbook on finitedimensional timeinvariant 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 finitedimensional, timeinvariant 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. … MSTI can be properly deemed an essential addition to the personal library of any researcher in systems theory. … MSTI 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 controlsystems 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 finitedimensional timeinvariant 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)
 Table of contents (5 chapters)


Mathematical Models
Pages 172

Introduction to State Space Theory
Pages 73192

Stability Theory
Pages 193368

Perturbation Theory
Pages 369516

Uncertain Systems
Pages 517713

Table of contents (5 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Mathematical Systems Theory I
 Book Subtitle
 Modelling, State Space Analysis, Stability and Robustness
 Authors

 Diederich Hinrichsen
 Anthony J. Pritchard
 Series Title
 Texts in Applied Mathematics
 Series Volume
 48
 Copyright
 2005
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783540264101
 DOI
 10.1007/b137541
 Hardcover ISBN
 9783540441250
 Softcover ISBN
 9783642039409
 Series ISSN
 09392475
 Edition Number
 1
 Number of Pages
 XVI, 804
 Number of Illustrations
 180 b/w illustrations
 Topics