Under the convex lifting for the state partitions, this paper studies the robust piecewise affine (PWA) control laws for linear discrete-time systems with state and input constraints. In particular, unlike the study of perturbations of state space partitions in vertex or half-plane representations, each state partition in this study is the smallest perturbation element. Practically, a maximum admissible region collection (MARC) is defined to inscribe the maximum perturbation region of each state partition. Based on MARC, which guarantees the postive invariance of the original controller, a fragility of convex lifting (FCL) is proposed to realize a robust PWA control with an implicit controller form. A numerical example illustrates the effectiveness of the new robust PWA controller.