This paper improves some results in [Antonio Sala, Carlos Ari?o, Asymptotically necessary and sufficient conditions for stabilityand performance in fuzzy control: applications of Polya’s theorem, Fuzzy Sets and Systems 158 (2007) 2671-2686]. In the relaxationof the stability results, only a smaller number of artificial decision variables are required. Thus, we obtain the equivalent stabilityresults, with lower requirement on the computation.