Abstract
In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model of the initial system, which is insensitive or has minimal sensitivity to the disturbances. The relations involved in designing the interval observer, which has minimal dimensions and estimates the prescribed linear function of the original system state vector, were obtained. The theoretical results were illustrated by a practical example.