On the question of the weak invariance of sets with respect to a differential inclusion generated by a control system

A differential inclusion generated by a control system is considered on a finite time interval. Questions concerning the property of weak invariance of sets with respect to the differential inclusion are investigated. For sets in the space of positions of the control system that are not weakly invariant with respect to the differential inclusion, a numerical characteristic is introduced, which estimates the degree of the (weak) noninvariance of a set, i.e., the weak invariance defect of this set with respect to the differential inclusion.