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, 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 book is also suitable for established researchers in systems theory as well as those just beginning in the field.

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 ofstability, 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)

Zusammenfassung

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 ofstability, 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)

Inhalt
Mathematical Models.- Introduction to State Space Theory.- Stability Theory.- Perturbation Theory.- Uncertain Spaces.- Appendix: Linear Algebra.- Complex Analysis.- Convolutions and Transforms.- Linear Operators.