This book, "Delay Compensation for Nonlinear, Adaptive, and PDE Systems" by Miroslav Krstic, addresses the control of systems with input and output delays, extending traditional predictor feedback methods to nonlinear systems, adaptive control, and partial differential equations (PDEs). It introduces a PDE-ODE cascade system approach for handling input delays, leading to constructive control design and quantitative stability analysis. The book also extends predictor feedback to systems with unknown delays and actuator dynamics modeled by more complex PDEs than simple transport PDEs. The book covers various topics, including the treatment of input and output delays as transport PDEs, the development of methods for compensating heat and wave PDE dynamics, and the design of observers for systems with similar sensor dynamics. It also discusses the extension of predictor feedback to nonlinear systems and adaptive control, as well as the challenges of stabilizing systems with unknown delays. The book is intended for researchers and engineers working on control of delay systems, including graduate students and specialists in delay systems. It provides a comprehensive overview of the latest developments in the field, including new paradigms for delay research. The book is not a standalone textbook but can be used as supplementary material in various graduate courses. The book includes a detailed introduction to delay systems, a historical overview of backstepping, and a discussion on the comparison of delay systems with PDEs. It also covers topics such as inverse optimal redesign, robustness to delay mismatch, time-varying delay, and adaptive control. The book is written for a technical audience with a background in control theory and mathematics, and it includes appendices that summarize key concepts such as Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection, and Bessel functions. The book is a research monograph that provides a collection of tools and techniques applicable to open problems in control theory.This book, "Delay Compensation for Nonlinear, Adaptive, and PDE Systems" by Miroslav Krstic, addresses the control of systems with input and output delays, extending traditional predictor feedback methods to nonlinear systems, adaptive control, and partial differential equations (PDEs). It introduces a PDE-ODE cascade system approach for handling input delays, leading to constructive control design and quantitative stability analysis. The book also extends predictor feedback to systems with unknown delays and actuator dynamics modeled by more complex PDEs than simple transport PDEs. The book covers various topics, including the treatment of input and output delays as transport PDEs, the development of methods for compensating heat and wave PDE dynamics, and the design of observers for systems with similar sensor dynamics. It also discusses the extension of predictor feedback to nonlinear systems and adaptive control, as well as the challenges of stabilizing systems with unknown delays. The book is intended for researchers and engineers working on control of delay systems, including graduate students and specialists in delay systems. It provides a comprehensive overview of the latest developments in the field, including new paradigms for delay research. The book is not a standalone textbook but can be used as supplementary material in various graduate courses. The book includes a detailed introduction to delay systems, a historical overview of backstepping, and a discussion on the comparison of delay systems with PDEs. It also covers topics such as inverse optimal redesign, robustness to delay mismatch, time-varying delay, and adaptive control. The book is written for a technical audience with a background in control theory and mathematics, and it includes appendices that summarize key concepts such as Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection, and Bessel functions. The book is a research monograph that provides a collection of tools and techniques applicable to open problems in control theory.