This paper studies the problems of stability analysis of Takagi-Sugeno free fuzzy systems with time-varying uncertainties. In our prior study, we represented the time-varying uncertainty incurred in characteristic interval matrices in terms of the stability of Takagi-Sugeno free fuzzy systems with consequent parameter uncertainty. Based on Mayer's convergent theorem for powers of single interval matrix and its generalization, we further proposed some sufficient conditions for the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be globally asymptotically stable. By employing the products of vertex matrices of interval matrices, this paper establishes some results for the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be globally asymptotically stable. Moreover, a numerical example for the Takagi-Sugeno free fuzzy systems with consequent parameter uncertainty to be globally asymptotically stable is included. Finally, a unique situation for the Takagi-Sugeno free fuzzy system to be globally asymptotically stable within "n iterations" is derived as well, where n relates to the dimension of interval matrices.