Under the vertex representation for the state partitions, this paper studies the fragility of piecewise affine (PWA) control laws for constrained discrete-time linear systems. In particular, the aim is to evaluate the impact of uncertainty in the representation of statespace partition. Practically, the notion of coupled vertex sensitivity (CVS) is defined to inscribe the joint uncertainty in the vertex positioning. This novel concept reduces the computational complexity and the conservativeness of the construction compared to the use of independent vertex perturbation through the iterative procedure using the existing results. A numerical example illustrated the effectiveness of our work.