Zubov's method is a technique to characterize the domain of attraction of locally asymptotically stable equilibria of an ordinary differential equation (ODE) as the sublevel set of an appropriate Hamilton-Jacobi equation. If the ODE is subject to control and perturbation, it is natural to ask for the set of initial states which can be asymptotically controlled to a given equilibrium regardless of the perturbation acting on the system. In this talk we show how Zubov's method can be generalized to this differential game setting by using the framework of viscosity solutions of Hamilton-Jacobi-Isaacs equations. A particular feature of our approach is that a priori we do not impose Isaacs' condition. Instead, we give an interpretation of both the upper and the lower value of the game by means of appropriate "upper" and "lower" generalizations of the controllability domains and of the required local controllability conditions. As a consequence, we show that under the usual Isaacs condition the respective controllability domains as well as the local controllability assumptions coincide. Joint work with Oana Serea, Perpignan