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This section contains the front matter for the book, including the title page, preface and table of contents. We also collect here some links that may be useful for instructors who are planning to use this book for a course. The preface of the book is presented in its entirety below, with some additional markup to link to the material in this wiki.

Textbook Contents

Preface (pdf, 28Sep12)

  • Titlepage and Copyright
  • Preface
  • Table of Contents

Teaching Materials

Supplemental Information


This book provides an introduction to the basic principles and tools for design and analysis of feedback systems. It is intended to serve a diverse audience of scientists and engineers who are interested in understanding and utilizing feedback in physical, biological, information, and economic systems. To this end, we have chosen to keep the mathematical prerequisites to a minimum while being careful not to sacrifice rigor in the process. Advanced sections, marked by the "dangerous bend" symbol
shown to the right, contain material that is of a more advanced nature and can be skipped on first reading.

This book was originally developed for use in an experimental course at Caltech involving students from a wide variety of disciplines. The course consisted of undergraduates at the junior and senior level in traditional engineering disciplines, as well as first and second year graduate students in engineering and science. This included graduate students in biology, computer science and economics, requiring a broad approach that emphasized basic principles and did not focus on applications in any one given area. A detailed web site has been prepared as a companion to this text:

The web site contains a database of frequently asked questions, supplemental examples and exercises, and lecture materials for a course based on this text. It also contains the MATLAB and other source code for every example in the book, as well as MATLAB libraries to implement the techniques described in the text.

Textbook scope

This book is intended to serve a broad spectrum of audiences and is organized in a slightly unusual fashion compared to many other books on feedback and control. In particular, we introduce a number of concepts in the text that are normally reserved for second year courses on control (and hence often not available to students who are not control systems majors).

This has been done at the expense of certain "traditional" topics, which we felt that the astute student could learn on their own (and are often explored through the exercises). Examples of topics that we have included are nonlinear dynamics, Lyapunov stability, reachability and observability, and fundamental limits of performance and robustness. Topics that we have de-emphasized include root locus techniques, lead/lag compensation (although this is essentially covered in Chapters 10 (PID Control) and 11 (Loop Shaping), and detailed rules for generating Bode and Nyquist plots by hand.

Overview of the contents

The first half of the book focuses almost exclusively on so-called "state-space" control systems. We begin in Chapter 2 (System Modeling) with a description of modeling of physical, biological and information systems using ordinary differential equations and difference equations. Chapter 3 (Examples) presents a number of examples in some detail, primarily as a reference for problems that will be used throughout the text. Following this, Chapter 4 (Dynamic Behavior) looks at the dynamic behavior of models, including definitions of stability and more complicated nonlinear behavior. We provide advanced sections in this chapter on Lyapunov stability, because we find that it is useful in a broad array of applications (and frequently a topic that is not introduced until much later in one's studies).

The remaining three chapters of the first half of the book focus on linear systems, begining with a description of input/output behavior in Chapter 5 (Linear Systems). In Chapter 6 (State Feedback), we formally introduce feedback systems by demonstrating how state space control laws can be designed. This is followed in Chapter 7 (Output Feedback) by material on output feedback and estimators. Chapters 6 and 7 introduce the key concepts of reachability and observability, which give tremendous insight into the choice of actuators and sensors, whether for engineered or natural systems.

The second half of the book presents material that is often considered to be from the field of "classical control." This includes the transfer function, introduced in Chapter 8 (Transfer Functions), which is a fundamental tool for understanding feedback systems. Using transfer functions, one can begin to analyze the stability of feedback systems using loop analysis, which allows us to reason about the closed loop behavior (stability) of a system from its open loop characteristics. This is the subject of Chapter 9 (Loop Analysis), which revolves around the Nyquist stability criterion.

In Chapters 10 (PID Control) and 11 (Loop Shaping), we again look at the design problem, focusing first on proportional-integral-derivative (PID) controllers and then on the more general process of loop synthesis. PID control is by far the most common design technique in control systems and a useful tool for any student. The chapter on loop synthesis introduces many of the ideas of modern control theory, including the sensitivity function. In Chapter 12 (Robust Performance), we pull together the results from the second half of the book to analyze the fundamental tradeoffs between robustness and performance. This is also a key chapter illustrating the power of the techniques that have been developed.

Use in courses

The book is designed for use in a 10-15 week course in feedback systems that can serve to introduce many of the key concepts that are needed in a variety of disciplines. For a 10 week course, Chapters 1-6 and 8-11 can each be covered in a week's time, with some dropping of topics from the final chapters. A more leisurely course, spread out over 14-15 weeks, could cover the entire book, with two weeks on modeling (Chapter 2) -- particularly for students without much background in ordinary differential equations -- and two weeks on loop analysis (Chapter 9) or robustness and performance (Chapter 12).

In choosing the set of topics and ordering for the main text, we necessarily left out some tools which will cause many control systems experts to raise their eyebrows (or choose another textbook). Overall, we believe that the early focus on state space systems, including the concepts of reachability and observability, are of such importance to justify trimming other topics to make room for them. We also included some relatively advanced material on fundamental tradeoffs and limitations of performance, feeling that these provided such insight into the principles of feedback that they could not be left for later. Throughout the text, we have attempted to maintain a balanced set of examples that touch many disciplines, relying on the supplements for more discipline specific examples and exercises. Additional notes covering some of the "missing" topics are available on the web.

One additional choice that we felt was very important was the decision not to make use of Laplace transforms in this book. While this is by far the most common approach to teaching feedback systems in engineering, many students in the natural and information sciences may lack the necessary mathematical background. Since Laplace transforms are not required in any essential way, we have only made a few remarks to tie things together for students with that background. Of course, we make tremendous use of transfer functions, which we introduce through the notion of response to exponential inputs, an approach we feel is much more accessible to a broad array of scientists and engineers.


The authors would like to thank the many people who helped during the preparation of this book. The idea for writing this book came in part from a report on future directions in control [Mur03] to which Stephen Boyd, Roger Brockett, John Doyle and Gunter Stein were ma jor contributers. Kristi Morgenson and Hideo Mabuchi helped teach early versions of the course at Caltech on which much of the text is based and Steve Waydo served as the head TA for the course taught at Caltech in 2003-04 and provide numerous comments and corrections. Finally, we would like to thank Caltech, Lund University and the University of California at Santa Barbara for providing many resources, stimulating colleagues and students, and a pleasant working environment that greatly aided in the writing of this book.

Karl Johan Åström Richard M. Murray
Lund, Sweden Pasadena, California

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