In this article, we are studying the non-linear e ects in a single-phase H-bridge inverter. The PWM control is related to a current feedback control. We are proposing an analytical model, which is a piecewise linear map. The distinctive feature of this study lies in the investigation of the map's properties. This investigation allows for the analytical determination of the ®xed points, their domains of stability, and of the bifurcation points. More precisely, we will show that some of these bifurcations are discontinuous. The analysis is performed while keeping in mind the current controller's tuning. In this particular setting, we will show that all the bifurcations are of a certain type: border collision bifurcations. Although we are treating the appearance of chaos in a converter, the work presented stays close to the preoccupations of the engineer, because the particularities of the digital control are shown as an advantage. Moreover, we have strived to comment on the di erent modes observed, periodic or not, by underlying their practical interest or disadvantages.

Abstract:On the path to an energy transition away from fossil fuels to sustainable sources, the European Union is for the moment keeping pace with the objectives of the Strategic Energy Technology-Plan. For this trend to continue after 2020, scientific breakthroughs must be achieved. One main objective is to produce solar fuels from solar energy and water in direct processes to accomplish the efficient storage of solar energy in a chemical form. This is a grand scientific challenge. One important approach to achieve this goal is Artificial Photosynthesis. The European Energy Research Alliance has launched the Joint Programme "Advanced Materials & Processes for Energy Applications" (AMPEA) to foster the role of basic science in Future Emerging Technologies. European researchers in artificial photosynthesis recently met at an AMPEA organized workshop to define common research strategies and milestones for the future. Through this work artificial photosynthesis became the first energy research sub-field to be organised into what is designated "an Application" within AMPEA. The ambition is to drive and accelerate solar fuels research into a powerful European field -in a shorter time and with a broader scope than possible for individual or national initiatives. Within AMPEA the Application Artificial Photosynthesis is inclusive and intended to bring together all European scientists in relevant fields. The goal is to set up a thorough and systematic programme of directed research, which by 2020 will have advanced to a point where commercially viable artificial photosynthetic devices will be under development in partnership with industry.