ON LIMIT-CYCLES AND THE DESCRIBING FUNCTION-METHOD IN PERIODICALLY SWITCHED CIRCUITS

This paper begins with an examination of existence, uniqueness, and st ability of limit cycles in periodically switched circuits. The motivat ion comes from the field of power electronics where switched circuit m odels composed of passive elements, independent sources, and ideal swi tches are studied. The paper then studies the describing function meth od for computation of limit cycles in these switched circuits. Typical power circuit models have nonlinear elements with characteristics tha t do not satisfy a Lipschitz continuity condition. As a result of thes e nonsmooth characteristics, previously developed justifications for t he describing function method are not applicable. The present paper de velops a justification for the describing function method that relies on the incrementally passive characteristics of the network elements c omprising typical power electronic circuit models. This justification holds for nonsmooth circuit nonlinearities, and takes the form of a se t of asymptotically convergent bounds on the errors incurred with the describing function method. In particular, the developed bounds become arbitrarily tight as the number of harmonics included in the analysis increases.