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This paper presents a controller synthesis method to stabilize piecewise-affine (PWA) slab systems based on invariant sets. Inspired by the theory of sliding modes, sufficient stabilization conditions are cast as a set of Linear Matrix Inequalities (LMIs) by proper choice of an invariant set which is a target sliding surface. The method has two steps: the design of the attractive sliding surface and the design of the controller parameters. While previous approaches to PWA controller synthesis are cast as Bilinear Matrix Inequalities (BMIs) that can, in some cases, be relaxed to LMIs at the cost of adding conservatism, our method leads naturally to a convex formulation. Furthermore, the LMIs obtained in this paper have lower dimension when compared to other methods because the dimension of the closed-loop state space is reduced. A numerical example on flutter suppression is included to demonstrate the effectiveness of the approach.