The reconfigurable power electronic converters (RPECs) are a new generation of systems, which modify their physical configuration in terms of a desired input or output operation characteristic. This kind of converters is very attractive in terms of versatility, compactness, and robustness. They have been proposed in areas such as illumination, transport electrification (TE), eenewable energy (RE), smart grids and the internet of things (IoT). However, the resulting converters operate in switched variable operation-regions, rather than over single operation points. As a result, there is a complexity increment on the modeling and control stage such that traditional techniques are no longer valid. In order to overcome these challenges, this paper proposes a kind of switched polytopic controller (SPC) suitable to stabilize an RPEC. Modeling, control, numerical and practical results are reported. To this end, a 400 W positive synchronous bi-directional buck/boost converter is used as a testbed. It is also shown, that the proposed converter and robust controller accomplish a compact, modular and reliable design during different working configuration, operation points and load changes.