The first step toward the development of a unified approach to the analysis and synthesis of control systems based on the use of comparison systems is the establishment of a relationship between the comparison principle and the invariance or contractivity. In this chapter, it is shown that the positive invariance or contractivity of a connected set represented by sublevel sets is equivalent to the existence of a monotone comparison system admitting a polyhedral set as a positively invariant or contractive set, respectively. This general result is then used to establish conditions of positive invariance and contractivity for specific classes of dynamical systems. It is also shown that the comparison principle can be used to compute positively invariant or contractive sets of reduced size by inserting new components in their representation by sublevel sets.