SUBTLETIES IN THE AVERAGING OF HYBRID SYSTEMS WITH APPLICATIONS TO POWER ELECTRONICS

Dither signals are commonly used in electronics for implementing different type of modulations in power converters, which represent a very interesting class of hybrid systems. It was recently shown that a nonsmooth dithered system can be approximated by an averaged system provided that the dither frequency is sufficiently high and that the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. This result is exploited in this paper for power converters. Averaged models corresponding to various shapes of dither signal are analyzed, showing that dither with Lipschitz continuous amplitude distribution function can be used to adapt the equivalent gain of the power converter.