Period adding with symmetry breaking/recovering in a power inverter with hysteresis control

In the present work, we investigate a period adding structure observed in a discontinuous 1D map modeling the behavior of a DC–AC H-bridge inverter with hysteresis control. Supported by experimental measurements from a laboratory prototype, we demonstrate that the structure is partially affected by bistability, so that for some parameter values the system has a single attracting cycle while for other parameter values a pair of attracting cycles of the same period exists. We show that the reason for possible bistability is related to the symmetry of the underlying model. Then, by means of symbolic dynamics, we explain which of the cycles are affected by bistability and which are not.