The paper addresses the problem of designing a stabilizing control for switched affine systems with unknown parameters. We formulate the problem both in the case where the set of affine subsystems is finite and also in the case where the set of affine subsystems is not finite and given by a convex polytope, i.e., the convex hull of finitely many affine subsystems. The main contribution is a switched and adaptive control design methodology with a global asymptotic stability property. The difficulty is related to the fact that the equilibrium point is unknown a priori. We propose an observer-based control strategy that uses a parameter estimate to update the control law in real time. A DC/DC Flyback converter is considered to illustrate the effectiveness of the proposed method. We also show that the proposed strategy preserves the stability property when the Flyback converter works in the so-called discontinuous conduction mode (DCM).