Linear Systems

"...A comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control."

- IEEE Transactions on Automatic Control

"[The authors] have contributed an expertly written and high quality textbook...and are to be congratulated.... Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference."

- Automatica

Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook. The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control. Linear Systems is written as a textbook for a challenging one-semester graduate course; a solutions manual is available to instructors upon adoption of the text. The book’s flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual.

For a treatment of linear systems that focuses primarily on the time-invariant case using streamlined presentation of the material with less formal and more intuitive proofs, see the authors’ companion book entitled A Linear Systems Primer.

• Signal
• algorithm
• algorithms
• communication
• integrated circuit
• stability
• static-induction transistor
• systems theory

From the reviews:

"There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook! …The authors have used their mastery of the subject to produce a textbook that very effectively presents the theory of linear systems as it has evolved over the last thirty years. The result is a comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control."—IEEE Transactions on Automatic Control

"In assessing the present book as a potential textbook for our first graduate linear systems course, I find...[that] Antsaklis and Michel have contributed an expertly written and high quality textbook to the field and are to be congratulated…. Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference."—Automatica

"As the title indicates, the emphasis is on linear systems.… Coverage of the material on polynomial matrix descriptions is omitted in many linear systems courses, but its inclusion in the present book is a positive feature. Strong features of the book are: the mathematical details are carefully developed, while providing engineering general motivation for the development [of the theory]; numerous historical notes are provided, there are numerous end of chapter exercises, and there is a useful appendix on numerical considerations.… In summary, it is good to have this new version of the book by Antsaklis and Michel as an available part of the literature that treats fundamental mathematical aspects of linear systems. It should be a strong contender as a textbook for first year graduate engineering courses on linear systems and it should serve as a valuable reference on linear systems for a wide audience.—MathematicalReviews

"There exist many good books on linear systems…. Among them the book by P.J. Antsaklis and A.M. Michel occupies a special place. It is an interesting and original introduction to modern control systems theory. It contains also many interesting problems from advanced systems theory. According to the authors the primary aim of the book is…‘to provide an understanding of these fundamentals by emphasizing mathematical descriptions of systems and their properties. Our goal was to clearly present the fundamental concepts of system theory in a self-contained text.’ The goal was reached and performed by the authors in an excellent way….

At the end of each chapter basic references are given and many interesting examples are included to clarify the material of the chapter. The exercises introduce additional concepts and results giving additional insight [into] the material. This is an interesting, original, and excellent textbook. It can be recommended for first-year graduate students and advanced undergraduates in electrical engineering, electronics, and mechatronics who are interested in control system and signal processing."—Control and Cybernetics

"As the title indicates, the emphasis is on linear systems. The book is intended as a textbook for first year graduate students in engineering, but it should be of interest as a reference to a wider audience. … In fact, most course instructors are likely to appreciate the emphasis on the mathematical aspects of linear systems. In summary, it is good to have this new version of the book … . it should serve as a valuable reference on linear systems for a wide audience." (N. Harris McClamroch, MathSciNet, Issue 2006 k)

"The book … aiming to provide a textbook for first-year graduate and senior undergraduate students. … Numerous examples are given to illustrate the concepts and techniques covered in the book. … This book is an excellent additionto existing textbooks on linear systems theory. … The book is clearly written, and its presentation is transparent and smooth. It is an excellent textbook for a one-semester first-year graduate-level course on linear systems theory. … The book is also a useful reference for researchers and engineering practitioners." (Lihua Xie, IEEE Control Systems Magazine, August, 2009)

• Dept. of Electrical Engineering, University of Notre Dame, Notre Dame, USA

  Panos J. Antsaklis, Anthony N. Michel

Panos J. Antsaklis received his Ph.D. in Electrical Engineering from Brown University, where he was a Fulbright Scholar. His main research interests are in the area of systems and control, particularly in linear feedback systems and intelligent autonomous control systems, with emphasis on hybrid and discrete event systems and reconfigurable control. He is currently Professor of Electrical Engineering at the University of Notre Dame. He has held regular and visiting teaching and research positions at Imperial College of the University of London, Brown University, Rice University, MIT, the National Technical University of Athens, and the Technical University of Crete, Greece.

Dr. Antsaklis has been awarded a departmental outstanding teacher award and has been a keynote speaker at a number of conferences. He is also a Distinguished Lecturer of the IEEE Control Systems Society. Dr. Antsaklis has authored a number of publications in journals, conference proceedings, and books and has coedited five books as well. He has served on the editorial boards of several journals, including the IEEE Transactions on Automatic Control, IEEE Transactions on Neural Networks, and the Journal of Discrete Event Dynamic Systems, and he has been the guest editor of special issues in these and other journals. Dr. Ansaklis has served as program chair and general chair of major systems and control conferences, and he is an IEEE Fellow and the 1997 President of the IEEE Control Systems Society.

Anthony N. Michel holds a Ph.D. in Electrical Engineering from Marquette University, as well as a D.Sc. in Applied Mathematics from the Technical University of Graz, Austria. He has extensive industrial and academic experience, and his main research interests are in control systems, circuit theory, neural networks, and applied mathematics. He is currently the Frank M. Freiman Professor of Electrical Engineering and Dean of theCollege of Engineering at the University of Notre Dame.

Dr. Michel has coauthored five books as well as a number of journal articles, conference proceedings, and conference books. He is a former editor of the IEEE Transactions on Circuits and Systems, and he has held a variety of positions on the editorial boards of the IEEE Transactions on Automatic Control, IEEE Transactions on Neural Networks, Circuits, Systems and Signal Processing, and Neurocomputing, as well as other journals. He is a past president of the IEEE Circuits and Systems Society and has served on the executive committees of several professional organizations. Dr. Michel is also the recipient of numerous professional awards. He is a Fellow of the IEEE. In 1984 he received the IEEE Centennial Medal, and he also earned three IEEE paper prizes. He spent 1992 as a Fulbright Scholar at the Technical University of Vienna, and, most recently, he received the 1995 Technical Achievement Award of the IEEE Circuits and Systems Society.

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