This technical note considers the local stabilization problem for the class of switched affine systems. The main idea is to use an alternative representation of the switched affine system as a nonlinear system with input constraints. Switching laws can be derived by emulating locally classical controllers. It is shown that by restricting to local stabilization, the classical constraint on the existence of constant stable convex combinations may be easily avoided. The approach may be interpreted as a generalization where convex combinations defined as functions of the system state are being used. Constructive methods for deriving switching laws are proposed.