Fuzzy stability analysis using interlacing condition

A sufficient condition for asymptotical stability of a Takagi-Sugeno fuzzy control system is derived. The goal of the present investigation is to analyze the stability of fuzzy system via stability of relevant frozen-time systems. To this end, a norm-based switching control scheme is introduced to stabilize the fuzzy control system. It demonstrates that the property on continuous-root-dependence with respect to polynomial coefficients found in robustness theory plays a crucial role in deriving these important results. An one-shot procedure, which only requires the root locations of two polynomials, is given to determine the stability of a T-S fuzzy control system. One nonlinear example is demonstrated to show the validity of the proposed approach.