Main Article Content
In this paper, we consider differential systems of the following structure: at two consecutive time intervals the motion of the object is described by two different systems of differential equations. We study the controllability of the object described by such system from the initial set in one space to the given set in another space through so-called ''transition hypersurface''. The transition of an object from one space to another one is given by a certain reflection. Sufficient conditions of the controllability of such differential systems in the problem with phase space change are obtained. Approaches to the study of both nonlinear and linear systems are considered.