This book introduces the hybrid integrator-gain system (HIGS) as a promising approach for overcoming fundamental limitations of linear time-invariant (LTI) control systems. These limitations pose significant challenges in meeting the ever-increasing demands for accuracy, speed and reliability in high-precision positioning systems, including wafer scanners and other advanced mechatronic platforms. The working principle of the HIGS relies on switching dynamics that avoid hard state resets and produce continuous control signals, resulting in phase advantages over LTI integrators and offering practical performance benefits. Hybrid Integrator-Gain Systems contributes a comprehensive set of practical tools for the design and analysis of HIGS-based controllers with the aim of enabling substantial performance improvements beyond what is achievable with conventional LTI control. The material is organized into three parts:Part I formally introduces the concept of the HIGS and uses numerical examples to demonstrate that genuine performance advantages over LTI control can be achieved;Part II develops rigorous time- and frequency-domain tools for analysing robust stability and performance of feedback interconnections between LTI plants and HIGS-based controllers, addressing the challenges in closed-loop analysis and design introduced by the hybrid nature of these systems; andPart III focuses on practical design considerations and experimental validation of HIGS-based controllers applied to LTI systems. Hybrid Integrator-Gain Systems presents a framework for the design and analysis of HIGS-based control architectures for LTI systems. It demonstrates how appropriately designed HIGS controllers can push the performance of high-tech systems to levels unattainable with purely LTI approaches. Researchers and practitioners working in high-precision motion control, hybrid and switched control and related fields will find this book of considerable interest for its potential to advance control performance.