On approximations of time-delay control systems*

The paper deals with a dynamical system described by delay differential equations which is controlled under conditions of unknown disturbances. This system is approximated by a system of ordinary differential equations which is used as a leader. An aiming procedure between the delay and approximating systems is elaborated. The procedure is organized in such a way that the necessary proximity of motions of these systems is guaranteed by means of the delay system control and a certain part of the approximating system controls. Another part of the approximating system controls can be used to compensate disturbances in the initial delay system and to ensure the required quality of the control process. Thus, by using the elaborated aiming procedure, results of control theory for ordinary differential systems can be applied to delay differential systems.