On the Stability of Takagi–Sugeno Fuzzy Systems With Time-Varying Uncertainties

Abstract

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 uncertainties. 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. In this paper, we propose the notion of simultaneously nilpotent interval matrices to investigate the Takagi-Sugeno free fuzzy system with time-varying uncertainties to be strongly stable within steps, where relates to the dimension of interval matrices. Moreover, a unique situation for the deterministic Takagi-Sugeno free fuzzy system to be strongly stable within steps is derived as well, where relates to the dimension of characteristic matrices for the deterministic Takagi-Sugeno free fuzzy system.