Time delay systems are ubiquitous. They are found in controllers of all sorts, where information from sensors may undergo a delay (perhaps computational) before being used as control inputs. Some systems experience delays where the control structures do not respond instantaneously to input. Other fields where such systems may be found include biology, economics, and politics in general. Of course, we are currently undergoing the effects of time delay in the COVID-19 pandemic, where the delay is due to the incubation period of the virus.

This book focuses primarily on control systems with delays, and uses time domain (frequency) analysis as the primary framework to analyze a system’s stability. It is aimed at graduate students with some background in control systems, but the author also proposes that it may be used as a refresher.

There are 21 chapters divided into four sections, with each section containing an introductory chapter (chapters 1, 5, 10, and 16) and a summary discussion chapter (chapters 4, 9, 15, and 21). The summaries also point forward in the text, to indicate where specific topics are covered. Most of the chapters are quite short and nicely focused, which makes it easy to refer back to previous chapters when necessary. Each chapter also contains a concluding section that quickly summarizes the content.

There is a nice bibliography for the book as a whole. While there is an index, it is fairly minimal and many important concepts are not included, which makes things a bit more awkward for use as a reference. The text also contains some MATLAB code listings; these are supposedly available from the author’s website, although I was unable to locate them during a cursory examination of the site.

I have had graduate school exposure to control systems, but cannot claim more than a passing familiarity with the current literature on them. I found the book quite approachable, though, and after carefully reading the first section felt reasonably at home with the rest of the book. The writing is excellent and the mathematics is presented in an approachable way. Some of the figures are not as easy to interpret as they might be in color, but that’s inherent to a monochrome printing, and the discussion of the figures (most have very good captions) helps nicely.

The introductory and discussion chapters, as well as the summaries in each chapter, work excellently to frame each section and make it possible to approach each section as a unit. Combined with the short chapters, it divides the topic nicely into digestible bites.