Feedback Systems

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems.

Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.

• Covers the mathematics needed to model, analyze, and design feedback systems


• Serves as an introductory textbook for students and a self-contained resource for researchers


• Includes exercises at the end of every chapter


• Features an electronic solutions manual


• Offers techniques applicable across a range of disciplines

"A very useful addition to the literature on the basic principles and theory of feedback systems. This is a unique and excellent book. I believe it will appeal to a broad audience."—Elling W. Jacobsen, Royal Institute of Technology, Stockholm

"This book is a significant contribution. It provides an accessible treatment for a wide audience who would otherwise have to labor through difficult mathematical or engineering treatments. The only prerequisite is a basic understanding of differential equations and linear algebra."—Brian Ingalls, University of Waterloo

"[T]his is a refreshing text which is delightful to read, and which even experts in the area may find a valuable resource for its diverse applications, and exercises, and its clear focus on fundamental concepts that does not get side-tracked by technical details."---Matthias Kawski, Mathematical Reviews

"Åström and Murray have prepared a very well-written introductory work for scientific and engineering audiences. . . . In summary, this work is a valuable addition to the important area of control and feedback systems."---M.G. Prasad, Choice

"This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. . . . Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that use feedback in physical, biological, information, and economic systems. . . . Exercises are provided at the end of every chapter, and an accompanying electronic solutions manual is available."

"This book provides an interesting and original introduction to the design and analysis of feedback systems. It is addressed to engineers and scientists who are interested in feedback systems in physical, biological, information and social systems."---Tadeusz Kaczorek, Zentralblatt MATH