This paper presents a new parallel distributed compensation controller design approach for T–S (Takagi–Sugeno) fuzzy control systems with affine matched membership functions in the system and controller. In the new fuzzy control, affine transformed membership functions are adopted by scaling and biasing the original membership functions of the system. Stabilization and performance criterion of the closed-loop T–S fuzzy systems are obtained through a new parameterized linear matrix inequality, which is rearranged by affine matched membership functions. The conservativeness of stabilization condition for the T–S fuzzy system is significantly relaxed by utilizing the constraints condition of the controllers membership functions, which is determined from the difference of each transformed membership function. In addition, the controller gain is reconstructed by a decision variable separation technique with two different free weighting matrices without any scaling parameter. The superiority of proposed method is verified through numerical examples.

中文翻译：

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具有仿射匹配隶属度函数的 TS 模糊系统的新稳定准则

本文提出了一种新的并行分布式补偿控制器设计方法，用于在系统和控制器中具有仿射匹配隶属函数的 T-S（Takagi-Sugeno）模糊控制系统。在新的模糊控制中，通过对系统的原始隶属函数进行缩放和偏置，采用仿射变换隶属函数。闭环 T-S 模糊系统的稳定性和性能标准是通过新的参数化线性矩阵不等式获得的，该不等式由仿射匹配隶属函数重新排列。利用控制器隶属函数的约束条件，显着放宽了 T-S 模糊系统稳定条件的保守性，该约束条件由每个变换隶属函数的差异确定。此外，控制器增益由决策变量分离技术重建，具有两个不同的自由加权矩阵，没有任何缩放参数。通过数值算例验证了所提方法的优越性。