2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96501We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous.15 pages, 0 figures. For this revision, the authors added a remark about an alternative nonconstructive proof of the main resultOptimization and Controltext