This study focuses on the design of a \(\mathcal {H}_{\infty }\) controller for continuous Takagi–Sugeno (T–S) fuzzy systems employing a membership function (MF)-dependent Lyapunov function. For stability analysis, we address expressions that depend on the derivatives of the MFs by proposing a new inequality to constrain these expressions. Based on this inequality, we propose a switched controller with a state-dependent switching law, providing more efficient performance than single-gain control. In addition, we extend these results to use a homogeneous polynomial membership function-dependent (HPMFD) Lyapunov function, demonstrating its effectiveness not only in reducing conservatism but also in simplifying the computational complexity of the design conditions. Some examples are presented to show the performance of the proposed controller.
