The book is devoted to the presentation of methods for the analysis and synthesis of digital control systems and their elements. Mathematical models are considered, as well as definitions and criteria for the basic properties of discrete objects and digital control systems, such as controllability, observability, completeness, stability and stability reserves. Time characteristics and methods for studying the quality of digital systems in transient and steady-state mode are given. Much attention is paid to the conversion and interconnection of models into state variables and input-output digital systems.