Summary. In this article the problems of synthesis of discrete control systems with using the state feedback method were considered. To solve such problems, it is necessary to specify the desired roots of the characteristic equation of a closed system. For discrete control systems, this task is problematic.

The features of the choice of the desired characteristic equation of a closed system were analyzed and the dependence of the quality of the synthesized system on its parameters was investigated.

An analytical determination of the desired characteristic roots of the digital system, which provide the necessary quality of the controlled process was proposed.

For check analytical expressions, models of discrete control systems have been developed using the MATLAB / Simulink software package.

Key words: state variables, controllability, response time.