Stability issues of linear Takagi-Sugeno fuzzy modles are thoroughly investigated. At first, a systematic way of searching for a common symmetric positive definite P matrix (common P matrix in short), which is related to stability, is proposed for N subsystems which are under a pairwise commutativity assumption. Robustness issue under modeling uncertainty in each subsystem is then considered by proposing a quadratic stability criterion and a method of determining uncertainty bounds. Finally, it is shown that the pairwise commutative assumption can be in fact relaxed by interpreting the uncertainties as mismatch parts of non-commutative system matrices. Several examples show the validity of the proposed methods.