This note proposes an interval analysis approach to invariance control synthesis for switched nonlinear systems without assuming that the subsystems are stable or have common equilibrium points. Partition-based controllers are extracted via iterative computation of controlled invariant sets based on an interval branch-and-bound scheme. This method is guaranteed to be finitely determined and complete, provided that the switched system satisfies a robustly controlled invariance condition. Two examples drawn from practical applications are provided to show the effectiveness and efficiency of the proposed method.