The need for reconfigurable, high power density, and low-cost configurations of DC-DC power electronic converters (PEC) in areas such as the transport electrification and the use of renewable energy has spread out the requirement to incorporate in a single circuit several topologies, which generally result in an increment of complexity about the modeling, control, and stability analyses. In this paper, a reconfigurable topology is presented which can be applied in alterative/changing power conversion scenarios and consists of a reconfigurable Buck, Boost, and Buck-Boost DC-DC converter (RBBC). A unified averaged model of the RBBC is obtained, a robust controller is designed through a polytopic representation, and a Lyapunov based switched stability analysis of the closed-loop system is presented. The reported RBBC provides a wide range of voltage operation, theoretically from to volts with a single power source. Robust stability, even under arbitrarily fast (bounded) parameter variations and reconfiguration changes, is reported including numerical and experimental results. The main advantages of the converter and the robust controller proposed are simple design, robustness against abrupt changes in the parameters, and low cost.