This volume presents a particular aspect of control theory-stabilization of programmed motion. Methods of the construction and synthesis of stabilizing controls are introduced together with original results and useful examples. The problem of optimal stabilization control synthesis is solved for linear systems of difference equations with quadratic quality criterion.1. Stabilization of Programmed Motions in General 2. Stabilization in the Case of Discrete Information on the System State 3. Optimal Control of Linear Equations and Quadratic Quality Criteria 4. Stabilization of Variable Structure Systems.