On the difference approximation of the delay control system

Consideration was given to the difference approximation of the control system obeying a differential inclusion with retarded argument. Approximation of an ensemble of the trajectories of a differential inclusion by a sequence of ensembles of the trajectories of the corresponding difference (discrete) inclusions was investigated. Estimates enabling one to judge whether the approximating sequences converge were obtained. The possibility of applying the results obtained to one minimax problem of optimal control of the system under consideration was demonstrated.