Symbolic Analysis: A Practical Alternative Viewpoint of Border Collision

In this paper, a symbolic method is proposed for analyzing the bifurcation in switching power converters. This method focuses on the cyclic operation of the system which characterizes its bifurcation behavior. The concept of block sequence is introduced, which, in conjunction with the periodicity of the system, can be used to distinguish the various types of bifurcation behavior, e.g., “smooth” period doubling and “nonsmooth” border collision. The proposed method is applied, as an illustrative example, to develop 2-dimensional bifurcation diagrams for a voltage-mode controlled buck converter.