We investigate the problem of synthesizing robust controllers that ensure that the closed loop satisfies an input reach-while-stay specification, wherein all trajectories starting from some initial set I, eventually reach a specified goal set G, while staying inside a safe set S. Our plant model consists of a continuous-time switched system controlled by an external switching signal and plant disturbance inputs. The controller uses a state feedback law to control the switching signal in order to ensure that the desired correctness properties hold, regardless of the disturbance actions. Our approach uses a proof certificate in the form of a robust control Lyapunov-like function (RCLF) whose existence guarantees the reach-while-stay specification. A counterexample guided inductive synthesis (CEGIS) framework is used to find a RCLF by solving a ∃∀∃∀ formula iteratively using quantifier free SMT solvers. We compare our synthesis scheme against a common approach that fixes disturbances to nominal values and synthesizes the controller, ignoring the disturbance. We demonstrate that the latter approach fails to yield a robust controller over some benchmark examples, whereas our approach does. Finally, we consider the problem of translating the RCLF synthesized by our approach into a control implementation. We outline the series of offline and real-time computation steps needed. The synthesized controller is implemented and simulated using the Matlab(tm)/Simulink(tm) model-based design framework, and illustrated on some examples.