Abstract. We consider the problem of estimating the state of a discrete-time control system with bounded perturbations. The procedure of constructing the information sets in the form of polyhedra based on the mathematical theory of R-functions is proposed. To optimize the operation of the system, we propose to construct the set of the most probable values of coordinates of a system state as the set of points equidistant from the geometric boundary of the original information set.

Keywords: control system, bounded perturbation, information set, R-function.