Justification of the describing function method for periodically switched circuits

The author studies the describing function method for analysis of periodically switched circuits, such as those used in power electronic applications. Typical power circuit models have nonlinear elements that do not satisfy a Lipschitz continuity condition. As a result, classical averaging theory is not generally applicable to these switched systems. Furthermore, as a result of the nonsmooth characteristics of circuit nonlinearities, previously developed justifications for the describing function method are also not applicable. A justification is developed for the describing function method that relies on the incrementally passive characteristics of the network elements comprising typical power electronic circuits. The analysis generates explicit bounds on the error incurred with the describing function method