State space synthesis of discrete linear systems

The target of this paper is to draw attention to some important relations between different procedures of state space synthesis of discrete linear systems optimizing the quadratic cost function. Common form of the synthesis concerns one-dimensional and multi-dimensional control problems solved by Second Method of Lyapunov, Maximum Principle of Pontryagin and by Bellamn's Dynamic Programming. Emphasis is upon providing a comprehensive coverage that stresses general principles and integrates the well proved procedures into the overall picture.