This paper presents an efficient, offline method to simultaneously synthesize controllers and seek closed-loop Lyapunov functions for constrained piecewise affine systems on triangulated subsets of the admissible states. Triangulation refinements explore a rich class of controllers and Lyapunov functions. Since an explicit Lipschitz Lyapunov function is found, an invariant subset of the closed-loop region of attraction is obtained. Moreover, it is a control Lyapunov function, so minimum-norm controllers can be realized through online quadratic programming. It is formulated as a sequence of semi-definite programs. The method avoids computationally burdensome non-convex optimizations and a-priori design choices that are typical of similar existing methods.