Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities

This paper proposes a numerical stability analysis methodology for the singleton-type linguistic fuzzy control systems based on optimization techniques. First, it demonstrates that a singleton-type linguistic fuzzy logic controller (FLC) can be converted into a region-wise sector-bounded controller or, more generally, a polytopic system by quadratic programming (QP). Next, the convex optimization technique called linear matrix inequalities (LMI) is used to analyze the closed loop of the converted polytopic system. Finally, the applicability of the suggested methodology is highlighted via simulation results.