On a stable solution of the problem of disturbance reduction

We study the problem of active reduction of the influence of a disturbance on the output of a linear control system. We consider a system of linear differential equations under the action of an unknown disturbance and a control to be formed. Our goal is to design an algorithm for reducing the disturbance by means of an appropriate control on the basis of inaccurate measurements of the system phase coordinates. This algorithm should form a feedback control that would guarantee that the trajectory of a given system tracks the trajectory of the reference system, i.e., the system described by the same differential equations but with zero control and disturbance. We present an algorithm for solving this problem. The algorithm, based on the constructions of guaranteed control theory, is stable with respect to informational noises and computational errors.