Stability analysis is one of the most important issues in any control system. In recent years, Takagi-Sugeno (T-S) model has attracted many control-system designers because of having employed human knowledge, intelligence and also its flexibility in precise modeling. Two different approaches are proposed for the stability analysis of Takagi-Sugeno systems. In the first approach, stability analysis of continuous T-S fuzzy systems is discussed when the state matrices of the subsystems are pair-wise commutative. For this purpose, a systematic method is proposed in order to find the matrix P for these kinds of fuzzy systems. Then, the quadratic stability analysis is extended to the continuous time T-S fuzzy systems without this property. In the second approach, stability analysis is performed on systems with 2 2 state matrices. At first, the existing region of the common positive matrix P is determined. Subsequently, a special case of subsystems is considered where the state matrices are also symmetric. In this method, the diagonal part of the state matrices are considered as nominal matrices of the subsystems while the sub-diagonal parts are considered as the corresponding uncertainty for these subsystems. The uncertainty bound for the sub-diagonal entries is determined. The bound is calculated in such a way that the matrix P obtained from the diagonal part of the state matrices, if it does exist, remains a common positive definite matrix for the fuzzy system.