1Stability of switching circuits using complete-cycle solution matrices

Abstract — The appearance of nonlinear phenomena like bi-furcations and chaos in dc-dc converters are mainly studied by using the Poincare ́ map of the system. This paper presents an alternative method based on the eigenvalues of the state transition matrix over one full cycle which provides better insight of the system and its stability properties. The paper shows how the state transition matrix for a full cycle can be applied to a wide class of power electronic circuits to investigate the stability of various limit cycles and offers considerable advantages over other convectional methods without increasing the complexity of the analysis. Another advantage of this method is its ability to explain and predict the length of intermittent subharmonic phenomena which occur when these converters are coupled with spurious signals. I