Modeling and stability analysis of DC-DC buck converter via Takagi-Sugeno fuzzy approach

The DC-DC voltage-mode controlled buck converter is a nonlinear, nonsmooth system that presents different circuit topologies within one switching cycle. This paper develops a Takagi-Sugeno fuzzy approach for modeling this circuit to capture all the essential nonlinearities that occur in fast time scale. Based on the resulting model, we propose tractable mathematical stability analysis for identifying fast-scale instabilities of the converter, more specifically the edge of bifurcation phenomena, employing nonsmooth Lyapunov functions. The search for the Lyapunov functions are formulated as Linear Matrix Inequalities (LMI) feasibility problem which easily can be solved using up-to-date interior point methods.