On the averaging of a class of hybrid systems

Modeling abstraction and time-scale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a class of hybrid systems that are excited by high-frequency external signals. These systems arise in the modeling of switched power converters, mechanical systems with friction and quantized systems. For a quite general class of excitation signals, an averaging result is shown stating that the hybrid system can be approximated by a Lipschitz-continuous system. The approximation is in the order of the maximal repetition interval of the excitation signal.