Existence of horseshoe maps in current-mode controlled buck-boost dc/dc converters

In this paper, a buck-boost dc/dc converter under a typical current-mode control is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of the one-sided shift map, which implies positive entropy of the system and hence chaotic behavior. The essential tool is the horseshoe hypotheses proposed by Kennedy and Yorke, which will be reviewed prior to the discussion of the main finding. Moreover, the existence of chaos is also illustrated in the light of homoclinic intersections of stable and unstable manifolds.