On the controllability of a class of differential inclusions depending on a parameter

In this paper, we deal with the following stability problem: given a differential inclusion of the formx'F(t,x,), where is a parameter varying in a topological space , find conditions under which the set of all , such that the differential inclusion is controllable, is open in . Applying Theorem 3.1 of Ref. 3, we get a result in this direction, assuming, as leader hypotheses, thatF(t,·,) is a convex process, from into itself, and thatF(t,x,·) is lower semicontinuous.