Reducing conservativeness in stability conditions of affine fuzzy systems using fuzzy Lyapunov function

This paper presents the relaxed stability condition for the affine fuzzy system using the fuzzy Lyapunov function which is the Lyapunov function with the membership function. Based on Lyapunov-stability theory, the relaxed stability condition for the affine fuzzy system is derived and represented to linear matrix inequalities(LMIs) with added null product term. Slack matrix variables are considered to analyze further relaxed stability condition. Finally, a simulation example is given to illustrate the merits of the proposed methods.