In this paper, we introduce a hybridization-based feedback control synthesis method for potentially unstable nonlinear continuous-time systems. We construct a discretization and feedback control that ensures dissipation form of incremental input-to-state stability property that a number of abstraction-based control methods rely on or benefit from. This enables the use of these methods also for the case of potentially unstable systems, to achieve a reachability or a temporal logic specification. We furthermore show that the algorithm can also improve abstraction-based methods that do not rely on stability assumptions by reducing the number of constructed abstract states and non-deterministic transitions. We illustrate the benefits of our approach in simulations featuring a cart-pendulum.