The Proportional-Integral-Derivative (PID) controller operates the majority of modern control systems and has applications in many industries; thus any improvement in its design methodology has the potential to have a significant engineering and economic impact. Despite the existence of numerous methods for setting the parameters of PID controllers, the stability analysis of time-delay systems that use PID controllers remains extremely difficult and unclear, and there are very few existing results on PID controller synthesis. Filling a gap in the literature, this book is a presentation of recent results in the field of PID controllers, including their design, analysis, and synthesis. The focus is on linear time-invariant plants that may contain a time-delay in the feedback loop-a setting that captures many real-world practical and industrial situations. Emphasis is placed on the efficient computation of the entire set of PID controllers achieving stability and various performance specifications, which is important for the development of future software design packages, as well as further capabilities such as adaptive PID design and online implementation.