On the Dependence of the Attainable Set of Linear Controlled Objects on Disturbances

In the theory of optimal control, an important role is played by the attainable set of the controlled object $D(T)$ at a given time $T$. For example, this set is useful in studying the dynamical possibilities of the controlled object. We study the nature of dependence of the attainable set of a linear non-stationary controlled object on disturbances of its dynamic characteristics. We establish constructive sufficient conditions of a general form that guarantee that the change of the attainable set, in the Hausdorff metric, is small if the changes of dynamic characteristics of a linear non-stationary controlled object are small in a certain sense.