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 non-smooth dithered system can be approximated by an averaged system if the dither frequency is sufficiently high and that the amplitude distribution function of the dither is continuous and has bounded derivative. In power electronics, a large class of systems can be modeled as hybrid dynamical systems due to the presence of switching devices (for instance diodes or transistors) that "instantaneously" change the dynamical behavior of the system. This class of systems can be adequately represented by hybrid systems or nonlinear differential equations with discontinuous nonlinearities. One of the standard approaches for designing control algorithms for power converters is to use modulation schemes (e.g. pulse width modulation, PWM). © 2006 Elsevier Ltd All rights reserved.