On the stability issues of linear Takagi-Sugeno fuzzy models

Stability issues of linear Takagi–Sugeno (T–S) fuzzy models are investigated. We first propose a systematic way of searching for a common matrix, which, in turn, is related to stability for N subsystems that are under a pairwise commutative assumption. The robustness issue under uncertainty in each subsystem is then considered. We then show that the pairwise commutative assumption can, in fact, be relaxed by a similar approach as that for uncertainty. The result is applicable to a rather broad class of T–S models, which are non-Hurwitz and/or nonpairwise commutative.