This work deals with the design of fuzzy controllers for stabilization of continuous-time nonlinear systems subject to ${\mathcal{L}}_2$ disturbances, which are represented by nonlinear Takagi–Sugeno fuzzy models, i.e., Takagi–Sugeno fuzzy models with nonlinear consequents. A nonquadratic Lyapunov function is used to derive sufficient design conditions based on linear matrix inequality constraints as well as to reduce the conservativeness when compared to existing control approaches in the literature. Furthermore, the nonquadratic Lyapunov function is defined in terms of an integral membership function, which leads to a delayed nonquadratic ${\mathcal{L}}_2$-stabilization condition. This condition avoids the well-known difficulties in dealing with time derivatives of membership functions and/or path-independent conditions, found in most of the nonquadratic control approaches for continuous-time Takagi–Sugeno fuzzy models. Two numerical examples are performed to illustrate the reduction in conservativeness provided by the proposed approach.

这项工作涉及模糊控制器的稳定连续时间非线性系统的模糊控制器的设计。 ${\mathcal{大号}}_{\mathrm{2个}}$干扰由非线性Takagi–Sugeno模糊模型表示，即具有非线性后果的Takagi–Sugeno模糊模型。与文献中的现有控制方法相比，使用非二次Lyapunov函数可基于线性矩阵不等式约束导出足够的设计条件，并降低保守性。此外，根据积分隶属函数定义了非二次Lyapunov函数，这导致了延迟的非二次${\mathcal{大号}}_{\mathrm{2个}}$-稳定条件。这种条件避免了在处理隶属函数的时间导数和/或与路径无关的条件时众所周知的困难，在连续时间Takagi-Sugeno模糊模型的大多数非二次控制方法中都发现了这种困难。进行了两个数值示例，以说明所提出方法所提供的保守性降低。