M.E. Semenov, O.I. Kanishcheva, D.M. Prohorov, A.N. Gulin

Article is devoted to the approached construction of periodic decisions of systems of the operationally-differential equations describing dynamics of automatic control systems which feedback includes hysteresis parts. It is shown, that the initial problem is equivalent to a question on existence of a fixed point of the integrated operator operating in space of absolutely continuous vector functions. The method of the approached construction of steady fixed points of this operator, based on updating of the shuttle algorithm offered by M.A. Krasnoselskij and A.V. Pokrovskij is offered. The conditions providing a realizability and convergence are resulted. Estimations of accuracy are received. The correctness of the decisions received by offered algorithm, in relation to small indignations of parameters of systems is proved.