The main purpose of this chapter is to establish conditions of positive invariance and contractivity of sets represented in dual form \(\mathcal {Q}(w,g,r)\) . To this end, first, a new class of comparison systems, called dual w-comparison systems, are defined. Then it is shown that the positive invariance or contractivity of a set \(\mathcal {Q}(w,g,r)\) is related to the existence of a w-comparison system admitting \( \mathcal {P}(g,r)\) as a positively invariant or contractive set. This general result can be applied to many different classes of systems to study the positive invariance or contractivity of all types of sets represented in dual form. In the second part of this chapter, the foundations of a method for the enlargement of positively invariant or contractive sets represented in dual form are established.