Stabilization of Takagi-Sugeno fuzzy systems with time-varying uncertainties

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.