This book provides new insight on the problem of closed-loop performance and oscillations in discontinuous control systems, covering the class of systems that do not necessarily have low-pass filtering properties. The author provides a practical, yet rigorous and exact approach to analysis and design of discontinuous control systems via application of a novel frequency-domain tool: the locus of a perturbed relay system (LPRS). Presented are a number of practical examples applying the theory to analysis and design of discontinuous control systems from various branches of engineering, including electro-mechanical systems, process control, and electronics. A few chapters of the book are devoted to frequency-domain theory of sliding mode control, which is presented as a special type of discontinuous control. Discontinuous Control Systems is intended for readers who have knowledge of linear control theory and will be of interest to graduate students, researchers, and practicing engineers involved in systems analysis and design. TOC:Preface.- Part I. The Locus of a Perturbed Relay Systems Theory.- Servo Problem in Discontinuous Control Systems.- The Locus of Perturbed Relay System (LPRS) Theory.- Input-Output Analysis of Relay Servo Systems.- Analysis of Sliding Modes in the Frequency Domain.- Part II. Applications of the Locus of a Perturbed Relay System.- Relay Pneumatic Servomechanism Design.- Relay Feedback Test Identification and Autotuning.- Analysis of Analogue Differentiator and Dynamical Compensator Based on Sliding Mode.- Analysis of Sliding Mode Observers.- Analysis of Performance of Second-Order SM Control Algorithms.- Solutions.- References.- Index.