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Finite Dimensional Linear Systems

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by Roger W. Brockett


2015 / xvi + 244 pages / Softcover / ISBN 978-1-611973-87-7 / List Price $76.50 / SIAM Member Price $53.55 / Order Code CL74

Keywords: linear systems, feedback control, least squares theory, stability theory, differential equations

Preface to the Classics Edition;
Chapter 1: Linear Differential Equations;
Chapter 2: Linear Systems;
Chapter 3: Least Squares Theory;
Chapter 4: Stability;
Glossary of Notation;

Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential.

This book

  • touches upon many of the standard topics in applied mathematics;
  • develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas; and
  • contains a number of nontrivial examples and many exercises.

The book is recommended for students in their first year of graduate school. The topics covered form the core for advanced work in fields such as optimal control, estimation, stability, electrical networks, and the control of distributed systems.

About the Author
Roger W. Brockett is the An Wang Research Professor of Electrical Engineering and Computer Science in the School of Engineering and Applied Sciences at Harvard University. He taught for six years in the Electrical Engineering Department at MIT before joining the Harvard faculty in 1969, from which he retired in 2012. He has contributed to the theory of automatic control with work on stability, nonlinear control, feedback linearization, nonlinear estimation, pole placement, hybrid systems, and robotics. More recently his work has involved problems arising in the study of intelligent machines. Areas of particular interest include the problem of motion control, minimum attention control, synchronization, and the investigation of new paradigms in quantum control. Professor Brockett has been recognized with awards from the American Automatic Control Council, IEEE, ASME, and SIAM for his contributions to research and education. He is a fellow of the IEEE, SIAM, and AMS and is a member of the US National Academy of Engineering.

ISBN 9781611973877

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