This paper deals with the stability problem of continuous-time Takagi-Sugeno (T-S) fuzzy models. Based on the Tanaka and Sugeno theorem, a new systematic method is introduced to investigate the asymptotic stability of T-S models in case of having second-order and symmetric state matrices. This stability criterion has the merit that selection of the common positive-definite matrix P is independent of the sub-diagonal entries of the state matrices. It means for a set of fuzzy models having the same main diagonal state matrices, it suffices to apply the method once. Furthermore, the method can be applied to T-S models having certain uncertainties. We obtain bounds for the uncertainties under which the asymptotic stability of the system is guaranteed. The obtained bounds are shown to be tight. Finally, the maximum permissible uncertainty bounds are investigated. Several examples are given to illustrate the effectiveness of the proposed method.
Shekaramiz, Mohammad and Sheikholeslam, Farid, "On the Stability Analysis of Perturbed Continuous T-S Fuzzy Models" (2018). Electrical and Computer Engineering Faculty Publications. Paper 215.