Mathematische Nachrichten, vol.288, no.16, pp.1891-1899, 2015 (SCI-Expanded)
& Co. KGaA, Weinheim.In this paper the set of trajectories of the control system is investigated. It is assumed that the behavior of the control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have an integral constraint. An approximation of the set of trajectories by the set which consists of a finite number of trajectories is given. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated. © 2015 WILEY-VCH Verlag GmbH