Symbolic analysis of switching systems: Application to bifurcation analysis of dc/dc switching converters

Abstract—A symbolic method is proposed in this paper for analyzing the bifurcation behavior of switching nonsmooth systems. The proposed method focuses on the symbolic sequence describing the topological change of the system which characterizes its bifurcation behavior. The concept of block sequence is first introduced. Based on the block sequence, the smoothness of the Poincaré map is described. Moreover, two main theorems are given to detect border collision and standard bifurcations. Finally, a specific example of the buck switching converter is presented to illustrate the application of the proposed symbolic analysis method. Using the proposed method, two-dimensional (2-D) bifurcation diagrams, which can assist engineers in identifying regions of preferred or undesired operations in the select parameter space, can be easily obtained. Index Terms—Bifurcation, border collision, nonsmooth system, switching converter, symbolic analysis, symbolic sequence. I