1. Stability of equilibrium points. Kinds of stabily and instability. 2. Stability of linear systems with the variable matrix. 3. Stability of nonlinear systems via linearization. 4. Ljapunov direct method of stability. 5. Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points. 6. Application of difference equations. Multiple-room heating problem. Newton law of cooling. 7. Discrete equivalents of continuous systems. 8. Discrete control theory. 9. The controllability and the complete controllability. 10. Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm. 11. Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability. 12.–13. Stabilization of control by feedback.