The Art of Control Engineering by Ken Dutton, Steve Thompson, and Bill Barraclough (1997). This comprehensive volume provides an excellent introduction to control theory that balances theory and practical aspects. Be aware that the arrangement of topics within the book can make it difficult to follow the conceptual development. (If you have difficulties finding this book in the U.S., then look for it in the UK.)

Advanced PID Control by Karl Johan Åström and Tore Hägglund (2005). Despite its seemingly narrow title, this is an extremely comprehensive and accessible book on the practical problems that one is likely to encounter when developing real-world feedback systems. Although the text is very “hands on” and geared toward field work (mostly in the chemical industry), it provides much more than just heuristic rules of thumb. This book is not an introduction, but it should possibly be everyone’s second book on feedback systems. (The previous edition, entitled PID Controllers: Theory, Design, and Tuning, remains in print and is in some ways a more practical book.)

Essentials of Control by J. Schwarzenbach (1996). This mercifully short volume (only 140 pages) provides an easy-to-read introduction to feedback control. It covers similar material as the present book, but from a more scholarly perspective. Lots of worked math examples. (If you have difficulties finding this book in the U.S., look for it in the UK.)

Feedback Systems: An Introduction for Scientists and Engineers by Karl Johan Åström and Richard M. Murray (2008). This book is intended as a modern, comprehensive introduction to all things feedback, but the result is rather strange. The authors spend an inexplicable amount of space pursuing various preliminaries and obscure side topics even as fundamental material receives short shrift or is omitted altogether. An oversupply of disparate examples, and the attempt to treat frequency and state-space methods simultaneously, end up confusing the reader. There is a lot of valuable material here, but it can be difficult to pick out. (An unfortunate number of production glitches has slipped into the printed book, but a PDF of the complete text, including fixes to known errata, is freely available from the website of one of the authors.)

Feedback for Physicists: A Tutorial Essay on Control by John Bechhoefer (Reviews of Modern Physics, volume 77 (2005), pages 783–836). This is a review article for physicists, by a physicist. It takes a long view, emphasizing concepts rather than technical or mathematical detail. It is difficult reading but covers some topics not found elsewhere. Most valuable for its outsider’s point of view.

Schaum’s Outline of Feedback and Control Systems by Joseph DiStefano, Allen Stubberud, and Ivan Williams (2nd edition, 2011). Not a bad, if terse, introduction, with many worked problems. Covers classical (frequency) methods only, but it does so in detail.

Modern Control Engineering by Katsuhiko Ogata (5th edition, 2009). A standard, college-level textbook on control theory.

Control System Design: An Introduction to State-Space Methods by Bernard Friedland (2005). A compact and affordable introduction to state-space methods.

Feedback Control of Computing Systems by Joseph L. Hellerstein, Yixin Diao, Sujay Parekh, and Dawn M. Tilbury (2004). Applications of feedback methods to computer systems. Not for beginners.

Feedback Control Theory by John C. Doyle, Bruce A. Francis, and Allen R. Tannenbaum (1990). This book is not an introduction to feedback methods. Rather, it is a mathematical research monograph in which the authors summarize some of their results. A PDF of the complete book is available at no cost.

Complex Variables and Applications by James Ward Brown and Ruel V. Churchill (8th edition, 2008). There are many good books on complex analysis. This (relatively) short volume provides a concise yet accessible introduction. The treatment seems especially suitable for an application-minded audience.

Fourier Analysis and Its Applications by Gerald B. Folland (2009). This book is an outstanding introduction to transform methods (Fourier and Laplace transforms) and their application to differential equations. The presentation is very accessible and hands-on. (This book does require solid knowledge of complex numbers.)

An Introduction to Probability Theory and Its Applications, Volume 1 by William Feller (3rd edition, 1968). A classic treatment of basic probability theory.